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JEE Trigonometric Equations PYQs with Solutions

236 previous year questions from Trigonometric Equations (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

236 questionsMathematics2002–2026Answers + solutions

About Trigonometric Equations PYQs

Trigonometric Equations has 236 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from NTA Abhyas JEE Main (83), JEE Main (82), 99 Percentile Qs Bank for JEE Main (30) and 1 other source, spanning 2002 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 7
  • 2025: 8
  • 2024: 11
  • 2023: 8
  • 2022: 14
  • 2021: 13
  • 2020: 84
  • 2019: 8
  • 2018: 4
  • 2017: 1
  • 2016: 3
  • 2015: 2

Trigonometric Equations questions with solutions

1

Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I List-II (P) The number of elements in the set \ x ∈ [-π, π] : ^6 x + ^4 x = 1\ (1)

JEE Advanced 2026 Solution View → 2

Passage: Consider the curve C_1 given by y = e^ -x for x ∈ [0, 10π] , and the curve C_2 given by y = e^ -x ( x + x) for x ∈ [0, 10π] . Let n be the total number of points of

JEE Advanced 2026 Solution View → 3

Let S = \ θ ∈ (-2π, 2π) : θ + 1 = 3 θ\ . Then ∑_ θ ∈ S θ is equal to:

JEE Main 2026 Solution View → 4

If S = \ θ ∈ [-π, π] : θ (5θ)/(2) = 7θ (7θ)/(2)\ , then n(S) is equal to _______.

JEE Main 2026 Solution View → 5

Let S = \ x ∈ [-π, π] : x ( x + x) = a, a ∈ ℤ\ . Then n(S) is equal to :

JEE Main 2026 Solution View → 6

The number of elements in the set \ x ∈[0,180^ ∘ ]: (x+100^ ∘ )= (x+50^ ∘ ) x (x-50^ ∘ )\ is \_\_\_\_ .

JEE Main 2026 Solution View → 7

Number of solutions of 3 2 θ+8 θ+3 3 =0, θ ∈[-3 π, 2 π] is:

JEE Main 2026 Solution View → 8

The number of solutions of the equation 2 θ (θ)/(2)+ (5 θ)/(2)=2 ^3 (5 θ)/(2) in [-(π)/(2), (π)/(2)] is :

JEE Main 2025 Solution View → 9

If for θ ∈[-(π)/(3), 0] , the points (x, y)=(3 (θ+(π)/(3)), 2 (θ+(π)/(6))) lie on x y+α x+β y+γ=0 , then α^2+β^2+γ^2 is equal to :

JEE Main 2025 Solution View → 10

If 10 ^4 θ+15 ^4 θ=6 , then the value of 27 cosec^6 θ+8 ^6 θ 16 ^8 θ is:

JEE Main 2025 Solution View → 11

The number of solutions of equation (4- 3 ) x -2 3 ^2 x=- 4 1+ 3 , x ∈[-2 π, (5 π)/(2)] is

JEE Main 2025 Solution View → 12

The number of solutions of the equation 2 x+3 x=π, x ∈[-2 π, 2 π]-\ ± (π)/(2), ± (3 π)/(2)\ is

JEE Main 2025 Solution View → 13

If θ ∈[-(7 π)/(6), (4 π)/(3)] , then the number of solutions of 3 cosec^2 θ-2( 3 -1) cosec θ-4=0 , is equal to

JEE Main 2025 Solution View → 14

If θ ∈[-2 π, 2 π] , then the number of solutions of 2 2 ^2 θ+(2- 6 ) θ- 3 =0 , is equal to:

JEE Main 2025 Solution View → 15

The sum of all values of θ ∈[0,2 π] satisfying 2 ^2 θ= 2 θ and 2 ^2 θ=3 θ is

JEE Main 2025 Solution View → 16

Let f: ℝ arrow ℝ be a function defined by f(x)=\ array cc x^2 ((π)/(x^2)), & if x ≠ 0 0, & if x=0 array . Then which of the following statements is TRUE?

JEE Advanced 2024 Solution View → 17

Let (π)/(2) < x < π be such that x= -5 11 . Then ( (11 x)/(2))( 6 x- 6 x)+( (11 x)/(2))( 6 x+ 6 x) is equal to

JEE Advanced 2024 Solution View → 18

The number of solutions of ^2 x+(2+2 x-x^2) x-3(x-1)^2=0 , where -π ≤ x ≤ π , is________

JEE Main 2024 Solution View → 19

Suppose θ ε[0, (π)/(4)] is a solution of 4 θ-3 θ=1 . Then θ is equal to :

JEE Main 2024 Solution View → 20

Let S=\ ^2 2 θ:( ^4 θ+ ^4 θ) x^2+( 2 θ) x+( ^6 θ+ ^6 θ)=0. has real roots \ . If α and β be the smallest and largest elements of the set S , respectively, then 3((α-2)^2+(β-1)^2)

JEE Main 2024 Solution View → 21

The number of solutions of the equation 4 ^ 2 x - 4 ^ 3 x + 9 - 4cosx = 0; x ∈ [- 2π, 2π] is:

JEE Main 2024 Solution View → 22

If 2 ^ 3 x + sin2xcosx + 4sinx - 4 = 0 has exactly 3 solutions in the interval [0, (nπ)/(2)⌉, n ∈ N , then the roots of the equation x ^ 2 + nx + ( n - 3 ) = 0 belong to :

JEE Main 2024 Solution View → 23

The sum of the solutions x ∈ R of the equation 3cos2x + ^ 3 2x ^ 6 x - ^ 6 x = x ^ 3 - x ^ 2 + 6 is

JEE Main 2024 Solution View → 24

If α, - (π)/(2) < α < (π)/(2) is the solution of 4cosθ + 5sinθ = 1 , then the value of tanα is

JEE Main 2024 Solution View → 25

If 2 ^ 2 θ - 5secθ = 1 has exactly 7 solutions in the interval [0, (nπ)/(2)] , for the least value of n ∈ N then ∑ _ k = 1 ^ n k 2 ^ k is equal to :

JEE Main 2024 Solution View → 26

Let the set of all a ∈ R such that the equation cos2x + asinx = 2a - 7 has a solution be [ p, q ] and r = tan9 ° - tan27 ° - (1)/(cot63 °) + tan81 ° , then pqr is equal to

JEE Main 2024 Solution View → 27

For any y ∈ ℝ , let cot ^ - 1 (y) ∈ (0, π) and ^ - 1 (y) ∈ (- (π)/(2), (π)/(2)) . Then the sum of all the solutions of the equation ^ - 1 ( 6y 9 - y ^ 2 ) + cot ^ - 1 ( 9 - y ^ 2

JEE Advanced 2023 Solution View → 28

Let ^ - 1 (x) ∈ (- (π)/(2), (π)/(2)) , for x ∈ ℝ . Then the number of real solutions of the equation 1 + cos(2x) = 2 ^ - 1 (tanx) in the set (- (3π)/(2), - (π)/(2)) ∪ (- (π)/(2)

JEE Advanced 2023 Solution View → 29

The number of elements in the set S = \ θ ∈ [ 0, 2π ] : 3 ^ 4 θ - 5 ^ 2 θ - 2 ^ 6 θ + 2 = 0\ is

JEE Main 2023 Solution View → 30

Let S = \ x ∈ (- (π)/(2), (π)/(2)): 9 ^ 1 - ^ 2 x + 9 ^ ^ 2 x = 10\ and β = ∑ _ x ∈ S ^ 2 ((x)/(3)) , then (1)/(6) ( β - 14 ) ^ 2 is equal to

JEE Main 2023 Solution View → 31

The set of all values of λ for which the equation ^ 2 2x - 2 ^ 4 x - 2 ^ 2 x = λ

JEE Main 2023 Solution View → 32

Let f ( θ ) = 3( ^ 4 ((3π)/(2) - θ) + ^ 4 ( 3π + θ )) - 2(1 - ^ 2 2θ) and S = \ θ ∈ [ 0, π ] : f ^ ' ( θ ) = - 3 2 \ . If 4β = ∑ _ θ ∈ S θ then f ( β ) is equal to

JEE Main 2023 Solution View → 33

If m and n respectively are the numbers of positive and negative value of θ in the interval [- π, π] that satisfy the equation cos2 (θ)/(2) = cos3 (9θ)/(2) , then mn is equal to

JEE Main 2023 Solution View → 34

Let S = \ θ ∈ [ 0, 2π ) : tan(π cos θ) + tan(π sin θ) = 0\ , then ∑ _ θ ∈ S ^ 2 (θ + (π)/(4)) is equal to

JEE Main 2023 Solution View → 35

Let |M| denote the determinant of a square matrix M . Let g: [0, (π)/(2)] → ℝ be the function defined by g(θ) = f(θ) - 1 + f((π)/(2) - θ) - 1 where f(θ) = (1)/(2)| cases 1 & sinθ

JEE Advanced 2022 Solution View → 36

Consider the following lists: List- I List- II (I) \ x ∈ [- (2π)/(3), (2π)/(3)]: cosx + sinx = 1\ (P) has two elements (II) \ x ∈ [- (5π)/(18), (5π)/(18)]: 3 tan3x = 1\ (Q) has

JEE Advanced 2022 Solution View → 37

The number of elements in the set S = \ x ∈ ℝ: 2cos( x ^ 2 + x 6 ) = 4 ^ x + 4 ^ - x \ is

JEE Main 2022 Solution View → 38

Let S = \ θ ∈ ( 0, 2π ) : 7 ^ 2 θ - 3 ^ 2 θ - 2 ^ 2 2θ = 2\ . Then, the sum of roots of all the equations x ^ 2 - 2( ^ 2 θ + cot ^ 2 θ)x + 6 ^ 2 θ = 0θ ∈ S , is _______.

JEE Main 2022 Solution View → 39

Let S = [- π, (π)/(2)) - \ - (π)/(2), - (π)/(4), - (3π)/(4), (π)/(4)\ . Then the number of elements in the set A = \ θ ∈ S: tanθ(1 + 5 tan(2θ)) = 5 - tan(2θ)\ is _____ .

JEE Main 2022 Solution View → 40

If the sum of solutions of the system of equations 2 ^ 2 θ - cos2θ = 0 and 2 ^ 2 θ + 3sinθ = 0 in the interval [0, 2π] is kπ , then k is equal to _______.

JEE Main 2022 Solution View → 41

Let S = \ θ ∈ [0, 2π]: 8 ^ 2 ^ 2 θ + 8 ^ 2 ^ 2 θ = 16\ . Then n(S) + ∑ _ θ ∈ S (sec((π)/(4) + 2θ) cosec ((π)/(4) + 2θ)) is equal to:

JEE Main 2022 Solution View → 42

The number of solutions of |cosx| = sinx , such that - 4π ≤ x ≤ 4π is

JEE Main 2022 Solution View → 43

The number of solutions of the equation sinx = ^ 2 x in the interval (0, 10) is ______.

JEE Main 2022 Solution View → 44

The number of elements in the set S = θ ∈ [- 4π, 4π]: 3 ^ 2 2θ + 6cos2θ - 10 ^ 2 θ + 5 = 0 is ______.

JEE Main 2022 Solution View → 45

The number of solutions of the equation 2θ - ^ 2 θ + 2 = 0 in R is equal to ______.

JEE Main 2022 Solution View → 46

The number of values of x in the interval ((π)/(4), (7π)/(4)) for which 14 cosec ^ 2 x - 2 ^ 2 x = 21 - 4 ^ 2 x holds, is ______.

JEE Main 2022 Solution View → 47

The number of solutions of the equation cos(x + (π)/(3))cos((π)/(3) - x) = (1)/(4) ^ 2 2x , x ∈ [- 3π, 3π] is:

JEE Main 2022 Solution View → 48

Let S = \ θ ∈ [ - π, π ] - \ ± (π)/(2)\ : sin θ + tanθ = sin2θ\ . If T = ∑ _ θ ∈ S cos2θ , then T + n(S) is equal to

JEE Main 2022 Solution View → 49

If n is the number of solutions of the equation 2cosx(4sin((π)/(4) + x)sin((π)/(4) - x) - 1) = 1, x ∈ [0, π] and S is the sum of all these solutions, then the ordered pair (n, S)

JEE Main 2021 Solution View → 50

Let S be the sum of all solutions (in radians) of the equation ^ 4 θ + ^ 4 θ - sin θ = 0 in [ 0, 4π ] then (8S)/(π) is equal to

JEE Main 2021 Solution View → 51

The sum of solutions of the equation (cosx)/(1 + sinx) = |tan2x|, x ∈ (- (π)/(2), (π)/(2)) - \ - (π)/(4), (π)/(4)\ is:

JEE Main 2021 Solution View → 52

The number of distinct real roots of | cases sinx & cosx & cosx cosx & sinx & cosx cosx & cosx & sinx cases | = 0 in the interval - (π)/(4) ≤ x ≤ (π)/(4) is:

JEE Main 2021 Solution View → 53

The sum of all values of x in [ 0, 2π ] , for which sinx + sin2x + sin3x + sin4x = 0 , is equal to :

JEE Main 2021 Solution View → 54

The number of solutions of ^ 7 x + ^ 7 x = 1, x ∈ [ 0, 4π ] is equal to

JEE Main 2021 Solution View → 55

The solutions of the equation | cases 1 + ^ 2 x & ^ 2 x & ^ 2 x ^ 2 x & 1 + ^ 2 x & ^ 2 x 4sin2x & 4sin2x & 1 + 4sin2x cases | = 0, (0 < x < π), are

JEE Main 2021 Solution View → 56

The number of solutions of the equation | cotx | = cotx + (1)/(sinx) in the interval [ 0, 2π ] is

JEE Main 2021 Solution View → 57

The number of solutions of the equation x + 2tanx = (π)/(2) in the interval [0, 2π] is

JEE Main 2021 Solution View → 58

The number of roots of the equation, (81) ^ ^ 2 x + (81) ^ ^ 2 x = 30 in the interval [0, π] is equal to :

JEE Main 2021 Solution View → 59

If 3 ( ^ 2 x) = ( 3 - 1)cosx + 1 , then number of solutions of the given equation when x ∈ [0, (π)/(2)] is ________.

JEE Main 2021 Solution View → 60

If 0 < x, y < π and cosx + cosy - cos(x + y) = (3)/(2) , then sinx + cosy is equal to:

JEE Main 2021 Solution View → 61

All possible values of θ ∈ [0, 2π] for which sin2θ + tan2θ > 0 lie in :

JEE Main 2021 Solution View → 62

Let f: [0, 2] → ℝ be the function defined by f(x) = (3 - sin(2 ))sin( - (π)/(4)) - sin(3 + (π)/(4)) . If α, β ∈ [0, 2] are such that \ x ∈ [0, 2]: f(x) ≥ 0\ = [α, β] , then the

JEE Advanced 2020 Solution View → 63

Number of roots of the equation cos ^ 2 ⁡ x + 3 + 1 2 sin ⁡ x - 3 4 - 1 = 0 which lie in the interval [- π, π] is

NTA Abhyas JEE Main 2020 Solution View → 64

If the equation x^ 2 + 4 + 3sin ⁡ (ax + b) - 2x = 0 has atleast one real solution, where a , b ∈ [ 0, 2π ] , then one possible value of ( a + b ) can be equal to&

NTA Abhyas JEE Main 2020 Solution View → 65

The number of solutions, the equation ^ 4 x + ^ 4 x = sinxcosx has, in [ π, 5π ] is/are

NTA Abhyas JEE Main 2020 Solution View → 66

If 1 + sin ⁡ θ + ^ 2 ⁡ θ + ^ 3 ⁡ θ +... ∞ = 4 + 2 3 , 0 < θ < π, then

NTA Abhyas JEE Main 2020 Solution View → 67

If (1)/(6) sinθ , cosθ and tan ⁡ θ are in geometric progression, then the complete solution set of θ is

NTA Abhyas JEE Main 2020 Solution View → 68

The number of values of θ ∈ [(- 3π)/(2), (4π)/(3)] which satisfies the system of equations 2 sin ^ 2 θ + sin ^ 2 2θ = 2 and sin2θ + cos2θ = tanθ is

NTA Abhyas JEE Main 2020 Solution View → 69

If tan ⁡ (k + 1)θ = tan ⁡ θ , then the set of all the values of θ is&

NTA Abhyas JEE Main 2020 Solution View → 70

General solution of the equation tan^ 2 θ + sec2θ = 1 is

NTA Abhyas JEE Main 2020 Solution View → 71

The general solution of the system of equations ^ 3 x + ^ 3 ((2 π)/(3) + x) + ^ 3 ((4 π)/(3) + x) + (3)/(4) 2 x = 0 and cos ⁡ x ≠ 0 is

NTA Abhyas JEE Main 2020 Solution View → 72

The set x ∈ ℝ: cos ⁡ 2x + 2 ^ 2 ⁡ x = 2 is equal to

NTA Abhyas JEE Main 2020 Solution View → 73

Number of solutions of 2 ^ sin ( | x | ) = 3 ^ | cosx | in [ - π, π ] , is equal to

NTA Abhyas JEE Main 2020 Solution View → 74

Consider the equation lo g _ 2 sinx (1 + cosx) = 2, x ∈ [- (π)/(2), (3π)/(2)] . If the sum of the roots is (pπ)/(q), where G.C.D (p, q) = 1 , then the value of p ^ 2 + q ^ 2 is

NTA Abhyas JEE Main 2020 Solution View → 75

If the expression ( 1 + tan ⁡ x + ^ 2 ⁡ x ) ( 1 - cot ⁡ x + ^ 2 ⁡ x ) is positive, then the complete set of values of x is

NTA Abhyas JEE Main 2020 Solution View → 76

The number of ordered pairs ( x, y ) satisfying the equations y = 2sin ⁡ xandy = 5 x ^ 2 + 2x + 3 is/are

NTA Abhyas JEE Main 2020 Solution View → 77

If x and y are the solutions of the equation 5 + 8sin^ 2 x = 2y^ 2 - 8y + 21 , then the least possible value of x^ 2 y^ 3 is

NTA Abhyas JEE Main 2020 Solution View → 78

In the interval& (0, 2π) , sum of all the roots of the equation sin(π ~log _ 3 & ( 1 x& )) = 0 is

NTA Abhyas JEE Main 2020 Solution View → 79

If 0 ≤ x ≤ 2π, then the number of real values of x satisfying the equation 8 1 ^ si n ^ 2 x + 8 1 ^ co s ^ 2 x = 30 is

NTA Abhyas JEE Main 2020 Solution View → 80

If cosx - sinx = - (5)/(4) , where (π)/(2) < x < (3π)/(4) , then cot(x)/(2) & is equal to

NTA Abhyas JEE Main 2020 Solution View → 81

The number of solutions of the equation |cot ⁡ x| = cot ⁡ x + cosecx in [0,10π] is/are

NTA Abhyas JEE Main 2020 Solution View → 82

The set of all values of a for which the equation cos ⁡ 2x + asin ⁡ x = 2a - 7 has a solution is

NTA Abhyas JEE Main 2020 Solution View → 83

If cot ⁡ (α + β) =0, then sin ⁡ (α + +2β)is equal to

NTA Abhyas JEE Main 2020 Solution View → 84

The sum of the roots of the equation | 3 cos ⁡ x - sin ⁡ x| = 2 in [0,4π] is kπ , then the value of 6k is

NTA Abhyas JEE Main 2020 Solution View → 85

The total number of solution(s) of the equation 2x + 3tan ⁡ x = (5π)/(2) in x ∈ [0,2π]is/are equal to

NTA Abhyas JEE Main 2020 Solution View → 86

If _ x ⁡ sinx ≥ 2 and 0 ≤ x ≤ 3π , then the value of sinx lies in the interval

NTA Abhyas JEE Main 2020 Solution View → 87

The number of roots of the equation tan ⁡ x + sec ⁡ x =2 cos ⁡ x in [0, 4π] is

NTA Abhyas JEE Main 2020 Solution View → 88

For - (π)/(2) ≤ x ≤ (π)/(2), the number of points of intersection of curves y = cos ⁡ x and y = sin ⁡ 3x is

NTA Abhyas JEE Main 2020 Solution View → 89

If 0 < A < B < π, sin ⁡ A - sin ⁡ B = (1)/(2) and cos ⁡ A - cos ⁡ B = (3)/(2) , then the value of A + B is equal to

NTA Abhyas JEE Main 2020 Solution View → 90

cose c ^ 2 θ( cos ^ 2 θ - 3cos ⁡ θ + 2) ≥ 1, if θ belongs to

NTA Abhyas JEE Main 2020 Solution View → 91

Let f(x) = 25 ^ x 25 ^ x + 5 , then the number of solution(s) of the equation f(si n ^ 2 θ) + f(co s ^ 2 θ) = ta n ^ 2 θ, θ ∈ [0,10π] is/are

NTA Abhyas JEE Main 2020 Solution View → 92

If x and y are the solutions of the equation 12sin ⁡ x + 5cos ⁡ x = 2 y ^ 2 - 8y + 21 , then the value of 12cot((xy)/(2)) is (Given, |x| < π )

NTA Abhyas JEE Main 2020 Solution View → 93

The sum of the roots of the equation cos ⁡ 4x + 6 = 7cos ⁡ 2x in the interval [0,314] is λπ, then the numerical value of λ is

NTA Abhyas JEE Main 2020 Solution View → 94

If α ~and& β are the solutions of sinx = - (1)/(2) in [0,2π] and α ~and& γ are the solutions of cos ⁡ x = - 3 2 in [0,2π] , then the value of~ (α + β)/(|β - γ|) is equal to

NTA Abhyas JEE Main 2020 Solution View → 95

If α ~and& β are the solutions of cot ⁡ x = - 3 in [0,2π] and α ~and& γ are the solutions of cosec ⁡ x = - 2 in [0,2π], then the value of (|α - β|)/(β + γ) is equal to

NTA Abhyas JEE Main 2020 Solution View → 96

The value of 2α + β(0 < α, β < (π)/(2)), satisfying the equation cos ⁡ ⁡ ⁡ (α + β) = - (1)/(8) is equal to

NTA Abhyas JEE Main 2020 Solution View → 97

The value of a + b such that the inequality a ≤ 5cos ⁡ θ + 3cos(θ + (π)/(3)) + 3 ≤ b holds true for all the real values of θ is (equality holds on both sides atleast once for real

NTA Abhyas JEE Main 2020 Solution View → 98

The equation kcos ⁡ x - 3sin ⁡ x = k + 1 is solvable only if

NTA Abhyas JEE Main 2020 Solution View → 99

If |sin^ 2 x + 10 - x^ 2 | = |9 - x^ 2 | + 2sin^ 2 x + cos^ 2 x, then x lies in

NTA Abhyas JEE Main 2020 Solution View → 100

The number of solutions to the equation |2e^ sin ⁡ x - 3 - e^ 2sin ⁡ x | =| e^ sin ⁡ x - e^ 2sin ⁡ x - 1| in [0, 2π]is

NTA Abhyas JEE Main 2020 Solution View → 101

If 0 < α, β < π and cos ⁡ α + cos ⁡ β - cos(α + β) = (3)/(2) , then the value of 3 sin ⁡ α + cos ⁡ α is equal to

NTA Abhyas JEE Main 2020 Solution View → 102

The sum of all the values of x between 0 and 4π which satisfy the equation sinx 8co s ^ 2 x = 1 is kπ , then the value of (k)/(5) is equal to

NTA Abhyas JEE Main 2020 Solution View → 103

If x = 2nπ + tan^ - 1 (p)/(q) and y = r is a solution of the equation 12sin ⁡ x + 5cos ⁡ x = 2y^ 2 - 8y + 21, then the value of k, such that& p^ 2 + q^ 2 + kr^ 2 = 15, is equal to

NTA Abhyas JEE Main 2020 Solution View → 104

The number of solutions of the equation ta n ^ 2 x - se c ^ 10 x + 1 = 0 for x ∈ (0,20) is equal to

NTA Abhyas JEE Main 2020 Solution View → 105

If sin ⁡ x + cos ⁡ x = 7 2 , where x ∈ [0, (π)/(4)], then the value of tan(x)/(2) is equal to

NTA Abhyas JEE Main 2020 Solution View → 106

The equation tan^ 4 x - 2sec^ 2 x + a^ 2 = 0 will have at least one solution, if

NTA Abhyas JEE Main 2020 Solution View → 107

The number of solutions of the equation (lo g _ 2 cos ⁡ θ) ^ 2 + lo g _ (4)/(cos ⁡ θ) (16cos ⁡ θ) = 2 in the interval [0, 2π)is

NTA Abhyas JEE Main 2020 Solution View → 108

The sum of all the solutions in [0,100] for the equation sin ⁡ + cos ⁡ = 0 is

NTA Abhyas JEE Main 2020 Solution View → 109

If 0 < A < B < π, sin ⁡ A + sin ⁡ B = (3)/(2) and cos ⁡ A + cos ⁡ B = 1 2 , then A =

NTA Abhyas JEE Main 2020 Solution View → 110

If ^ 2 ⁡ (x + y) + ^ 2 ⁡ (x + y) = 1 - 2x - x^ 2 , then (where, n ∈ ℤ)

NTA Abhyas JEE Main 2020 Solution View → 111

General solution of the equation 4cot ⁡ 2θ + ^ 2 θ = ^ 2 ⁡ θ is (where, n ∈ ℤ )

NTA Abhyas JEE Main 2020 Solution View → 112

The number of solutions in the interval [0, π] of the equation sin ^ 3 ⁡ xcos ⁡ 3x + sin ⁡ 3x cos ^ 3 ⁡ x = 0 is equal to

NTA Abhyas JEE Main 2020 Solution View → 113

If cos ⁡ x = tan ⁡ y, cos ⁡ y = tan ⁡ z and cos ⁡ z = tan ⁡ x, then sin ⁡ x = 2sin ⁡ θ where θ is (where, x, y, z, θ are acute angles)

NTA Abhyas JEE Main 2020 Solution View → 114

The number of values of x lying in the interval (- 2π, 2π) satisfying the equation 1 + cos ⁡ 10xcos ⁡ 6x = 2 ^ 2 8x + ^ 2 8x is equal to

NTA Abhyas JEE Main 2020 Solution View → 115

The number of solutions of the equation sin ^ 3 ⁡ xcos ⁡ x + sin ^ 2 ⁡ x cos ^ 2 ⁡ x + cos ^ 3 ⁡ xsin ⁡ x + 1 = 0 in the interval [0, 2π] is equal to

NTA Abhyas JEE Main 2020 Solution View → 116

If sin ⁡ x + cos ⁡ y = (1)/(3) and cos ⁡ x + sin ⁡ y = (3)/(4) , then the value of tan ⁡ ((x - y)/(2))is equal to

NTA Abhyas JEE Main 2020 Solution View → 117

If 3 sin ⁡ x + cos ⁡ x - 2 = (y - 1) ^ 2 for 0 ≤ x ≤ 8π , then the number of values of the pair (x, y) is equal to

NTA Abhyas JEE Main 2020 Solution View → 118

The number of solutions of the equation ^ 2 ⁡ ( sin ⁡ x + 3) = 1 in [0,3π]is equal to

NTA Abhyas JEE Main 2020 Solution View → 119

The solution of the equation ^ 2 ⁡ x + ^ 2 ⁡ 3x = 1 is&

NTA Abhyas JEE Main 2020 Solution View → 120

The number of solutions of the equation ( 3 + cos ⁡ x) ^ 2 = 4 - 2 ^ 8 ⁡ x in [ 0, 9π)is equal to

NTA Abhyas JEE Main 2020 Solution View → 121

The number of values of x ∈ [-2π,2π] which satisfy the equation cosecx = 1 + cot ⁡ x is equal to

NTA Abhyas JEE Main 2020 Solution View → 122

If ^ 3 ⁡ θ - ^ 3 ⁡ θ sin ⁡ θ - cos ⁡ θ - cos ⁡ θ 1 + ^ 2 ⁡ θ - 2tan ⁡ ⁡ θ = - 1 (∀ θ ∈ [0, 2π]), then

NTA Abhyas JEE Main 2020 Solution View → 123

The number of values of the parameter α ∈ [0, 2π] for which the quadratic function (sin ⁡ α) x^ 2 + (2cos ⁡ α) x + (1)/(2)(cos ⁡ α + sin ⁡ α)is the square of a linear function is

NTA Abhyas JEE Main 2020 Solution View → 124

In the interval [- (π)/(2), (π)/(2)] , the equation log _ sin ⁡ θ ⁡ (cos ⁡ 2θ) = 2 has

NTA Abhyas JEE Main 2020 Solution View → 125

The number of ordered pairs (a, x) satisfying the equation sec ^ 2 ⁡ (a + 2)x + a^ 2 - 1 = 0, - π < x < π is

NTA Abhyas JEE Main 2020 Solution View → 126

If sin ⁡ 2A = (1)/(2) and sin ⁡ 2B = - (1)/(2), then which of the following is false?

NTA Abhyas JEE Main 2020 Solution View → 127

The solution of the equation ( ^ 2 ⁡ x - 1) ^ - 1 = 1 + cos ⁡ 2x is

NTA Abhyas JEE Main 2020 Solution View → 128

The number of ordered pairs (x, y) of real numbers satisfying the system of equations sin ⁡ x = sin ⁡ 2y and cos ⁡ x = sin ⁡ y , where 0 ≤ x, y ≤ π , is

NTA Abhyas JEE Main 2020 Solution View → 129

The total number of solutions of the equation sin ⁡ xtan ⁡ 4x = cos ⁡ x for all x ∈ (0, π) are

NTA Abhyas JEE Main 2020 Solution View → 130

If the number of principal solutions of the equation tan ⁡ (7 ⁡ x) = cot ⁡ (7 ⁡ x) is k , then (k)/(5) is equal to

NTA Abhyas JEE Main 2020 Solution View → 131

The number of solutions of the equation tan ⁡ x + sec ⁡ x = 2cos ⁡ x lying in the interval [0,5π] is

NTA Abhyas JEE Main 2020 Solution View → 132

The number of solutions of the equation lo g _ 2 sin ⁡ x ( 1 + cos ⁡ x ) = 2 in the interval [0, 5π] is

NTA Abhyas JEE Main 2020 Solution View → 133

Let 0 < θ _ 1 < θ _ 2 < θ _ 3 < … denotes the positive solutions of the equation 3 + 3cos ⁡ θ = 2 ^ 2 ⁡ θ . If θ _ 3 + θ _ 7 = aπ , where a is an integer, then the value of a is

NTA Abhyas JEE Main 2020 Solution View → 134

The solution set of x ∈ (- π, π) for the inequality sin ⁡ 2x + 1 ≤ cos ⁡ x + 2sin ⁡ x is

NTA Abhyas JEE Main 2020 Solution View → 135

If A = \ θ: 2 ^ 2 ⁡ θ + sin ⁡ θ ≤ 2\ and B = \ θ: (π)/(2) ≤ θ ≤ (3π)/(2)\ , then A ∩ B is equal to

NTA Abhyas JEE Main 2020 Solution View → 136

The number of solution of the equation ∑ _ r = 1 ^ 5 cos ⁡ (rx) = 0 lying in (0, π) is

NTA Abhyas JEE Main 2020 Solution View → 137

The number of values of x in the interval [0, 5π] satisfying the equation 3 sin ^ 2 ⁡ x - 7sin ⁡ x + 2 = 0 is

NTA Abhyas JEE Main 2020 Solution View → 138

The number of solution of ^ 2 ⁡ x + ^ 2 ⁡ 2x = 2 in [0,20] is equal to

NTA Abhyas JEE Main 2020 Solution View → 139

The number of solutions of the equation cot ⁡ xcos ⁡ x - 1 = cot ⁡ x - cos ⁡ x, ∀ x ∈ [0, 2π] is equal to

NTA Abhyas JEE Main 2020 Solution View → 140

The value of& x satisfying the equation |sin ⁡ xcos ⁡ x| + 2 + tan ^ 2 ⁡ x + cot ^ 2 ⁡ x = 3 &

NTA Abhyas JEE Main 2020 Solution View → 141

The solution set of the equation 4sin ⁡ ⁡ θ - 2cos ⁡ θ - 2 3 sin ⁡ θ + 3 = 0 in the interval (0, 2π) is

NTA Abhyas JEE Main 2020 Solution View → 142

The sum of roots of the equation ^ 4 x - ^ 2 xsinx + 2 ^ 2 x + sinx = 0 for 0 ≤ x ≤ 3π is equal to

NTA Abhyas JEE Main 2020 Solution View → 143

The number of solutions of the equation sinx ⋅ sin2x ⋅ sin3x ⋅ sin4x ⋅ sin5x = 0 in [0, π] is equal to

NTA Abhyas JEE Main 2020 Solution View → 144

The equation ^ 4 ⁡ x - ^ 4 ⁡ x + cos ⁡ 2x + α ^ 2 + α = 0 will have at least one solution, if

NTA Abhyas JEE Main 2020 Solution View → 145

The number of solutions of the equation tan ⁡ xsin ⁡ x - 1 = tan ⁡ x - sin ⁡ x, ∀ x ∈ [0,2π]is equal to.

NTA Abhyas JEE Main 2020 Solution View → 146

Let f(x) = sin ⁡ ( ⁡ x) and g(x) = cos ⁡ (2 ⁡ x) be two functions defined for x > 0 . Define the following sets whose elements are written in the increasing order: X = \ x: f(x) =

JEE Advanced 2019 Solution View → 147

Let f(x) = sin ⁡ ( ⁡ x) and g(x) = cos ⁡ (2 ⁡ x) be two functions defined for x > 0 . Define the following sets whose elements are written in the increasing order: X = \ x: f(x) =

JEE Advanced 2019 Solution View → 148

Let S be the set of all α ∈ R such that the equation, cos2x + = 2α - 7 has a solution. Then S is equal to:

JEE Main 2019 Solution View → 149

The number of solutions of the equation 1 + ^ 4 x = ^ 2 3x, x ∈ [- (5π)/(2), (5π)/(2)] is:

JEE Main 2019 Solution View → 150

All the pairs ( x, y ) , that satisfy the inequality 2 ^ ^ 2 x - 2sinx + 5 · 1 4 ^ ^ 2 y ≤ 1 also satisfy the equation:

JEE Main 2019 Solution View → 151

Let S = \ θ ∈ [- 2π, 2π]: 2 ^ 2 θ + 3sinθ = 0\ . Then the sum of the elements of S is:

JEE Main 2019 Solution View → 152

The sum of all values of θ ∈ (0, (π)/(2)) satisfying ^ 2 2θ + ^ 4 2θ = (3)/(4) is

JEE Main 2019 Solution View → 153

If 0 ≤ x < (π)/(2), then the number of values of x for which sinx - sin2x + sin3x = 0, is:

JEE Main 2019 Solution View → 154

The number of solutions of 3 x= 2 x , in the interval ((π)/(2), π) is

JEE Main 2018 Solution View → 155

Consider the following two statements. Statement p : The value of 120^ ^ ∘ can be divided by taking θ=240^ ^ ∘ in the equation 2 (θ)/(2)= 1+ θ - 1- θ . Statement q : The angles A

JEE Main 2018 Solution View → 156

If A and B are the roots of the quadratic equation, 3 x^2-10 x-25=0 then the value of 3 ^2(A+B)-10 (A+B) · (A+B)-25 ^2 (A+B) is

JEE Main 2018 Solution View → 157

If sum of all the solutions of the equation 8cosx · (cos((π)/(6) + x) · cos((π)/(6) - x) - (1)/(2)) = 1 in [0, π] is kπ , then k is equal to:

JEE Main 2018 Solution View → 158

Let α and β be non zero real numbers such that 2(cos ⁡ β - cos ⁡ α) + cos ⁡ ⁡ β = 1 . Then which of the following is/are true?

JEE Advanced 2017 Solution View → 159

Let S = \ x ∈ (- π, π): x ≠ 0, ± (π)/(2)\ . The sum of all distinct solution of the equation 3 sec ⁡ x + cosecx + 2(tan ⁡ x - cot ⁡ x) = 0 , in the set S is equal to

JEE Advanced 2016 Solution View → 160

Let P = \ θ: sinθ - cosθ = 2 cosθ\ and Q = \ θ: sinθ + cosθ = 2 sinθ\ , be two sets. Then

JEE Main 2016 Solution View → 161

If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cosx + cos2x + cos3x + cos4x = 0, is

JEE Main 2016 Solution View → 162

The number of distinct solutions of the equation (5)/(4) ^ 2 ⁡ 2x + ^ 4 ⁡ x + ^ 4 ⁡ x + ^ 6 ⁡ x + ^ 6 ⁡ x = 2 in the interval [ 0, 2π ] is

JEE Advanced 2015 Solution View → 163

If cosα + cosβ = (3)/(2)andsinα + sinβ = (1)/(2) and θ is the arithmetic mean of α and β, then sin2θ + cos2θ is equal to:

JEE Main 2015 Solution View → 164

For xϵ(0, π), the equation sin ⁡ x + 2sin ⁡ 2x - sin ⁡ 3x = 3 has

JEE Advanced 2014 Solution View → 165

If 2 θ+ θ=1(θ ≠ (π)/(2)) , then 7 θ+6 θ is equal to:

JEE Main 2014 Solution View → 166

The number of values of α in [0, 2π] for which 2 ^ 3 α - 7 ^ 2 α + 7sin α = 2 , is :

JEE Main 2014 Solution View → 167

Let A=\ θ: (θ)= (θ)\ and B=(θ: (θ)= 1\ be two sets. Then:

JEE Main 2013 Solution View → 168

The number of solutions of the equation 2 x-2 x+4 x=4 in the interval [0,5 π] is :

JEE Main 2013 Solution View → 169

The number of solutions of the equation, ^ -1 x=2 ^ -1 x (in principal values) is :

JEE Main 2013 Solution View → 170

Statement-1: The number of common solutions of the trigonometric equations 2 ^2 θ - 2 θ=0 and 2 ^2 θ-3 θ=0 in the interval [0,2 π] is two. Statement-2: The number of solutions of

JEE Main 2013 Solution View → 171

A value of x for which ( ^ -1 (1+x)) = ( ^ -1 x), is :

JEE Main 2013 Solution View → 172

Let θ, ϕ ∈[0,2 π] be such that 2 θ(1- ϕ)= ^ 2 θ × ( (θ)/(2)+ (θ)/(2)) ϕ-1, (2 π-θ)>0 and -1 < θ < - 3 2 , then ϕ cannot satisfy

JEE Advanced 2012 Solution View → 173

The equation e^ x -e^ - x -4=0 has

JEE Main 2012 Solution View → 174

Let f(x)=x^2 and g(x)= x for all x ∈ R . Then, the set of all x satisfying ( fogogof )(x)=(gogof)(x) , where (f ∘ g)(x)=f(g(x)) is

JEE Advanced 2011 Solution View → 175

Let P=\ θ: θ- θ= 2 θ\ and Q=\ θ: θ+ θ= 2 θ\ be two sets. Then,

JEE Advanced 2011 Solution View → 176

The positive integer value of n 3 satisfying the equation (1)/( ((π)/(n)))=(1)/( ((2 π)/(n)))+(1)/( ((3 π)/(n))) is

JEE Advanced 2011 Solution View → 177

If A= ^2 x+ ^4 x , then for all real x

JEE Main 2011 Solution View → 178

The number of all possible values of θ , where 0 θ π , for which the system of equations array r ( y+z) 3 θ=( x y z) 3 θ x 3 θ=(2 3 θ)/(y)+(2 3 θ)/(z) array and (x y z) 3 θ=(y+2

JEE Advanced 2010 Solution View → 179

The number of values of θ in the interval (-(π)/(2), (π)/(2)) such that θ ≠ (n π)/(5) for n=0, ± 1, ± 2 and θ= 5 θ as well as 2 θ= 4 θ is

JEE Advanced 2010 Solution View → 180

For 0 < θ < (π)/(2) , the solution(s) of ∑_ m=1 ^6 cosec[θ+((m-1) π)/(4)] cosec(θ+(m π)/(4))=4 2 is/are

JEE Advanced 2009 Solution View → 181

If ( ^4 x)/(2)+( ^4 x)/(3)=(1)/(5) , then

JEE Advanced 2009 Solution View → 182

The number of solutions of the pair of equations 2 ^2 θ- 2 θ=0 and 2 ^2 θ-3 θ=0 in the interval [0,2 π] is

JEE Advanced 2007 Solution View → 183

The set of values of θ satisfying the inequation 2 ^2 θ-5 θ+2>0 , where 0 < θ < 2 π , is

JEE Advanced 2006 Solution View → 184

The number of values of x in the interval [0,3 π] satisfying the equation 2 ^2 x+5 x-3=0 is

JEE Main 2006 Solution View → 185

If 0 < x < π and x+ x=(1)/(2) , then x is

JEE Main 2006 Solution View → 186

The number of solution of x+ x=2 x in [0,2 π) is

JEE Main 2002 Solution View → 187

If ^3 θ+ ^3((2 π)/(3)+θ)+ ^3((4 π)/(3)+θ)=α 3 θ , then α is equal to

99 Percentile Qs Bank for JEE Main Solution View → 188

If 6 θ=32 ^5 θ θ-32 ^3 θ θ+3 x then x is equal to :

99 Percentile Qs Bank for JEE Main Solution View → 189

The extreme values of 4 (x^2) \ left((π)/(3)+x^2) ((π)/(3)- x^2) over R, are

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∑_ k=1 ^3 ^2 ((2 k-1) (π)/(12)) is equal to

99 Percentile Qs Bank for JEE Main Solution View → 191

If cosec θ=(p+q)/(p-q) , then ((π)/(4)+(θ)/(4))is equal to

99 Percentile Qs Bank for JEE Main Solution View → 192

If 5 x+12 y=13 , then the maximum value of 5 x+12 y is :

99 Percentile Qs Bank for JEE Main Solution View → 193

If a ^2 θ+b ^2 θ=c , then ^2 θ is equal to

99 Percentile Qs Bank for JEE Main Solution View → 194

The set of solutions of the equation ( 3 -1) θ+( 3 +1) θ=2 is

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If f(x)= ^2 x+ ^2 2 x+ ^2 3 x , then the number of values of x ∈[0,2 π] for which f(x)=1 is

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The set of solutions of the system of equations aligned x+y & = (2 π)/(3) and x+ y & = (3)/(2), aligned where x, y are real, is

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If a ^2 θ+b ^2 θ=c , then ^2 θ is equal to

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The number of all the possible integral values of n>2 such that (π)/(2 n)+ (π)/(2 n)= n 2 is

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If (1)/(6) θ, θ and θ are in geometric progression, then the solution set of θ is

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The set of solutions of the equation ( 3 -1) θ+( 3 +1) θ=2 is

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Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)

Trigonometric Equations in other exams

NDA Trigonometric Equations (16)BITSAT Trigonometric Equations (22)