Quantrex Academy Quantrex AcademyPYQs with solutions · JEE · NEET · NDA

Home · JEE PYQs · Mathematics · Trigonometric Ratios & Identities

JEE Trigonometric Ratios & Identities PYQs with Solutions

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

189 questionsMathematics2002–2026Answers + solutions

About Trigonometric Ratios & Identities PYQs

Trigonometric Ratios & Identities has 189 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 189 questions in this list come from JEE Main (82), NTA Abhyas JEE Main (49), 99 Percentile Qs Bank for JEE Main (29) and 2 other sources, 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: 13
  • 2025: 5
  • 2024: 5
  • 2023: 4
  • 2022: 10
  • 2021: 7
  • 2020: 53
  • 2019: 10
  • 2018: 1
  • 2017: 2
  • 2016: 3
  • 2015: 1

Trigonometric Ratios & Identities questions with solutions

1

Let α = (1 - 2 ((π)/(11)))(1 - 2 ((3π)/(11)))(1 - 2 ((9π)/(11)))(1 - 2 ((27π)/(11)))(1 - 2 ((81π)/(11))) . Then the value of 5 - α^2 is _____________.

JEE Advanced 2026 Solution View → 2

If A = ( 3^∘)/( 9^∘) + ( 9^∘)/( 27^∘) + ( 27^∘)/( 81^∘) and B = 81^∘ - 3^∘ , then (B)/(A) is equal to _____.

JEE Main 2026 Solution View → 3

Let P = \ θ ∈ [0, 4π] : ^2θ ≠ 1\ and S = \ a ∈ ℤ : 2( ^8θ - ^8θ) 2θ = a^2, θ ∈ P\ . Then n(S) is:

JEE Main 2026 Solution View → 4

If ((π)/(18)) ((5π)/(18)) ((7π)/(18)) = K , then the value of ((10Kπ)/(3)) is :

JEE Main 2026 Solution View → 5

If (A-B) A + ^ 2 C ^ 2 ~A =1, ~A, ~B, C ∈(0, (π)/(2)) , then

JEE Main 2026 Solution View → 6

If x=(5)/(12) for some x ∈(π, (3 π)/(2)) , then 7 x( (13 x)/(2)+ (13 x)/(2))+ 7 x( (13 x)/(2)- (13 x)/(2)) is equal to

JEE Main 2026 Solution View → 7

The value of 3 cosec 20^ ∘ - 20^ ∘ 20^ ∘ 40^ ∘ 60^ ∘ 80^ ∘ is equal to

JEE Main 2026 Solution View → 8

The least value of ( ^ 2 θ-6 θ θ+3 ^ 2 θ+2) is

JEE Main 2026 Solution View → 9

Let (π)/(2) ((15 θ)/(2))( 8 θ+ 8 θ)+ ((15 θ)/(2))( 8 θ- 8 θ) is equal to

JEE Main 2026 Solution View → 10

Let α and β respectively be the maximum and the minimum values of the function f(θ)=4( ^ 4 ((7 π)/(2)-θ)+ ^ 4 (11 π+θ))-2( ^ 6 ((3 π)/(2)-θ)+ ^ 6 (9 π-θ)), θ ∈ R . Then α+2 β is

JEE Main 2026 Solution View → 11

Let (α+β)=-(1)/(10) and (α-β)=(3)/(8) , where 0<α<(π)/(3) and 0<β<(π)/(4) . If 2 α= 3(1-r 5 ) 11 (s+ 5 ) , r, s ∈ N , then r+s is equal to \_\_\_\_ .

JEE Main 2026 Solution View → 12

If ^ 2 48^ ∘ - ^ 2 12^ ∘ ^ 2 24^ ∘ - ^ 2 6^ ∘ = α+β 5 2 , where α, β ∈ ℕ , then α+β is equal to \_\_\_\_\_

JEE Main 2026 Solution View → 13

The value of cosec 10^ ∘ - 3 10^ ∘ is equal to :

JEE Main 2026 Solution View → 14

Let α= 1 60^ ∘ 61^ ∘ + 1 62^ ∘ 63^ ∘ +…+ 1 118^ ∘ 119^ ∘ Then the value of ( cosec 1^ ∘ α )^2 is __________

JEE Advanced 2025 Solution View → 15

If x+ ^2 x=1, x ∈(0, (π)/(2)) , then ( ^ 12 x+ ^ 12 x)+3( ^ 10 x+ ^ 10 x+ ^8 x+ ^8 x)+( ^6 x+ ^6 x) is equal to :

JEE Main 2025 Solution View → 16

If ∑_ r=1 ^ 13 \ (1)/( ((π)/(4)+(r-1) (π)/(6)) ((π)/(4)+(r π)/(6)))\ =a 3 +b, a, b ∈ Z , then a^2+b^2 is equal to :

JEE Main 2025 Solution View → 17

The value of ( 70^ ∘ ) ( 10^ ∘ 70^ ∘ -1) is

JEE Main 2025 Solution View → 18

If (π)/(2) ≤ x ≤ (3 π)/(4) , then ^ -1 ((12)/(13) x+(5)/(13) x) is equal to

JEE Main 2025 Solution View → 19

Let | θ (60-θ) (60+θ)| ≤ (1)/(8), θ ε[0,2 π] . Then, the sum of all θ ε[0,2 π] , where 3 θ attains its maximum value, is :

JEE Main 2024 Solution View → 20

If the value of 3 36^ ∘ +5 18^ ∘ 5 36^ ∘ -3 18^ ∘ is a 5 -b c , where a, b, c are natural numbers and gcd(a, c)=1 , then a+b+c is equal to :

JEE Main 2024 Solution View → 21

If x=-(3)/(5) , where π < x < (3 π)/(2) , then 80( ^2 x- x) is equal to

JEE Main 2024 Solution View → 22

If tanA = 1 x( x ^ 2 + x + 1) , tanB = x x ^ 2 + x + 1 and tanC = ( x ^ - 3 + x ^ - 2 + x ^ - 1 )(1)/(2), 0 < A, B, C < (π)/(2) , then A + B is equal to:

JEE Main 2024 Solution View → 23

For α, β ∈ (0, (π)/(2)) let 3sin ( α + β ) = 2sin ( α - β ) and a real number k be such that tanα = tanβ . Then the value of k is equal to

JEE Main 2024 Solution View → 24

96cos(π)/(33)cos(2π)/(33)cos(4π)/(33)cos(8π)/(33)cos(16π)/(33) is equal to

JEE Main 2023 Solution View → 25

The value of 36(4 ^ 2 9 ^ ∘ - 1)(4 ^ 2 27 ^ ∘ - 1)(4 ^ 2 81 ^ ∘ - 1)(4 ^ 2 243 ^ ∘ - 1) is

JEE Main 2023 Solution View → 26

The value of tan 9 ^ o - tan 27 ^ o - tan 63 ^ o + tan 81 ^ o is _____.

JEE Main 2023 Solution View → 27

If tan15 ° + (1)/(tan75 °) + (1)/(tan105 °) + tan195 ° = 2a , then the value of (a + (1)/(a)) is :

JEE Main 2023 Solution View → 28

Let α and β be real numbers such that - (π)/(4) < β < 0 < α < (π)/(4) . If sin(α + β) = (1)/(3) and cos(α - β) = (2)/(3) , then the greatest integer less than or equal to

JEE Advanced 2022 Solution View → 29

Let α = ∑ _ k = 1 ^ ∞ ^ 2k ((π)/(6)) . Let g: [0, 1] → ℝ be the function defined by g(x) = 2 ^ ax + 2 ^ a(1 - x) . Then, which of the following statements is/are TRUE?

JEE Advanced 2022 Solution View → 30

Let S = \ θ ∈ (0, (π)/(2)): ∑ _ m = 1 ^ 9 sec(θ + (m - 1)(π)/(6))sec(θ + (mπ)/(6)) = - 8 3 \ . Then

JEE Main 2022 Solution View → 31

The value of 2sin(π)/(22)sin(3π)/(22)sin(5π)/(22)sin(7π)/(22)sin(9π)/(22) is equal to:

JEE Main 2022 Solution View → 32

If cotα = 1 and secβ = - (5)/(3) , where π < α < (3π)/(2) and (π)/(2) < β < π , then the value of tan(α + β) and the quadrant in which α + β lies, respectively are

JEE Main 2022 Solution View → 33

α = sin36 ° is a root of which of the following equation

JEE Main 2022 Solution View → 34

The value of cos((2π)/(7)) + cos((4π)/(7)) + cos((6π)/(7)) is equal to

JEE Main 2022 Solution View → 35

16sin(20 °)sin(40 °)sin(80 °) is equal to

JEE Main 2022 Solution View → 36

If ^ 2 (10 °)sin(20 °)sin(40 °)sin(50 °)sin(70 °) = α - (1)/(16)sin(10 °) , then 16 + α ^ - 1 is equal to _____.

JEE Main 2022 Solution View → 37

The value of 2sin12 ° - sin72 ° is

JEE Main 2022 Solution View → 38

cosec 18 ° is a root of the equation:

JEE Main 2021 Solution View → 39

A 10 inches long pencil AB with mid point C and a small eraser P are placed on the horizontal top of a table such that PC = 5 inches and ∠ PCB = ^ - 1 ( 2 ) . The acute angle

JEE Main 2021 Solution View → 40

The value of 2sin((π)/(8))sin((2π)/(8))sin((3π)/(8))sin((5π)/(8))sin((6π)/(8))sin((7π)/(8)) is :

JEE Main 2021 Solution View → 41

If sinθ + cosθ = (1)/(2), then 16(sin(2θ) + cos(4θ) + sin(6θ)) is equal to:

JEE Main 2021 Solution View → 42

The value of cot(π)/(24) is:

JEE Main 2021 Solution View → 43

If 15 ^ 4 α + 10 ^ 4 α = 6, for some α ∈ R, then the value of 27 sec ^ 6 α + 8 cosec ^ 6 α is equal to :

JEE Main 2021 Solution View → 44

The number of integral values of k for which the equation 3sinx + 4cosx = k + 1 has a solution, k ∈ R is _______.

JEE Main 2021 Solution View → 45

If L = ^ 2 ((π)/(16)) - ^ 2 ((π)/(8)) and M = ^ 2 ((π)/(16)) - ^ 2 ((π)/(8))

JEE Main 2020 Solution View → 46

If the equation ^ 4 θ + ^ 4 θ + λ = 0 has real solutions for θ then λ lies in interval

JEE Main 2020 Solution View → 47

The value of ^ 3 ((π)/(8)) . cos((3π)/(8)) + ^ 3 ((π)/(8)) . sin((3π)/(8)) is:

JEE Main 2020 Solution View → 48

If 2 sinα 1 + cos2α = (1)/(7) and (1 - cos2β)/(2) = 1 10 , α, β ∈ (0, (π)/(2)) , then tan(α + 2β) , is equal to

JEE Main 2020 Solution View → 49

If A, B, C are in arithmetic progression and B = (π)/(4), then tan ⁡ Atan ⁡ Btan ⁡ C =

NTA Abhyas JEE Main 2020 Solution View → 50

Let y = ^ - 1 ( 8) - ^ - 1 ( 1 0) + ^ - 1 ( 1 2) - sec ^ - 1 (sec 9) + cot ^ - 1 (cot 6) - cosec ^ - 1 (cosec 7) . If y simplifies to a π + b then (a - b) is

NTA Abhyas JEE Main 2020 Solution View → 51

If the value of (1 + tan 1 ^ o )(1 + tan 2 ^ o )(1 + tan 3 ^ o )… … … . ( 1 + tan 44 ^ o ) ( 1 + tan 45 ^ o ) is 2 ^ λ ~ ,& then the sum of the digits of the number λ is

NTA Abhyas JEE Main 2020 Solution View → 52

If a ^ 2 ⁡ x + b ^ 2 ⁡ x = c, b ^ 2 ⁡ y + a ^ 2 ⁡ y = d and atan ⁡ x = btan ⁡ y, then a^ 2 b^ 2 is equal to (Here a, b, c and& d are distinct)

NTA Abhyas JEE Main 2020 Solution View → 53

If p = ^ 2 ⁡ x + ^ 4 ⁡ x , then

NTA Abhyas JEE Main 2020 Solution View → 54

The value of 2 ^ 2 ⁡ θ + 4cos ⁡ (θ + α)sin ⁡ ⁡ θ + cos ⁡ 2 ( α + θ ) is

NTA Abhyas JEE Main 2020 Solution View → 55

The value of the expression (2 ( sin1 ° + sin2 ° + sin3 ° +........ + sin89 ° ))/(2 ( cos1 ° + cos2 ° + cos3 ° +........ + cos44 ° ) + 1) and is equal to

NTA Abhyas JEE Main 2020 Solution View → 56

If cos α + β = a , α + β = b and α - β = 2 θ , then ( 3 θ)/( θ) is equal to

NTA Abhyas JEE Main 2020 Solution View → 57

The value of (1 + cos(π)/(8))(1 + cos (3π)/(8))(1 + cos(5π)/(8))(1 + cos(7π)/(8)) is equal to

NTA Abhyas JEE Main 2020 Solution View → 58

Let the maximum and minimum value of the expression 2 ^ 2 ⁡ θ + cos ⁡ θ + 1 is M and m respectively, then the value of [(M)/(m)] is, (where [.] is the greatest integer function)

NTA Abhyas JEE Main 2020 Solution View → 59

ta n ^ 6 2 0 ^ o - 33ta n ^ 4 2 0 ^ o + 27ta n ^ 2 2 0 ^ o + 4 =

NTA Abhyas JEE Main 2020 Solution View → 60

If π < θ < (3π)/(2) and cos ⁡ θ = - (3)/(5) , then tan ((θ)/(4))& is equal to

NTA Abhyas JEE Main 2020 Solution View → 61

Let f(n) = (sin ⁡ 1) × (sin ⁡ 2) ×..... sin(n), ∀ n ∈ ℕ , then the number of elements in the set A = \ f(1), f(2),.......... , f(6)\ & that are positive are

NTA Abhyas JEE Main 2020 Solution View → 62

The difference between the greatest and the least possible value of the expression 3 - cos ⁡ x + ^ 2 ⁡ x is&

NTA Abhyas JEE Main 2020 Solution View → 63

If E = ^ 2 ⁡ 71 ^ o + ^ 2 ⁡ 49 ^ o + cos ⁡ 71 ^ o cos ⁡ 49 ^ o , then the value of 10E is equal to

NTA Abhyas JEE Main 2020 Solution View → 64

Let f(x) = max\ tan ⁡ x,cot ⁡ x\ . Then the number of roots of the equation f (x) = (1)/(2)in (0,2π)is

NTA Abhyas JEE Main 2020 Solution View → 65

The value of the expression 1 + cosec(π)/(4) + cosec(π)/(8) + cosec(π)/(16) is equal to

NTA Abhyas JEE Main 2020 Solution View → 66

If& (2sin ⁡ α)/(1 + cos ⁡ α + sin ⁡ α) = (3)/(4) , then the value of (1 - cos ⁡ α + sin ⁡ α)/(1 + sin ⁡ α) is equal to

NTA Abhyas JEE Main 2020 Solution View → 67

If sin ⁡ A and cos ⁡ A are the roots of the equation 4x^ 2 - 3x + a = 0, sin ⁡ A + cos ⁡ A + tan ⁡ A + cot ⁡ A+ sec ⁡ A + cosecA = 7 and 0 < A < (π)/(2), then the value of a must

NTA Abhyas JEE Main 2020 Solution View → 68

If 4sin ⁡ 27 ^ o = α - β , then the value of α + β is

NTA Abhyas JEE Main 2020 Solution View → 69

If cos ⁡ 5θ = 5cosθ ⁡ - 20 ^ 3 ⁡ θ + a ^ 5 ⁡ θ + b , then the value of a + b is equal to

NTA Abhyas JEE Main 2020 Solution View → 70

The maximum value of the expression sin ⁡ ^ 2 θ (∀ θ ∈[0, π]) is

NTA Abhyas JEE Main 2020 Solution View → 71

The value of tan ⁡ 63 ^ o - cot ⁡ 63 ^ o is equal to

NTA Abhyas JEE Main 2020 Solution View → 72

If sin((23π)/(24)) = 2 p - q - 1 4 r , then the value of (p^ 2 + q^ 2 - r^ 2 ) is equal to

NTA Abhyas JEE Main 2020 Solution View → 73

If 4cos ⁡ 36 ^ o + cot(7(1)/(2) ∘) = n _ 1 + n _ 2 + n _ 3 + n _ 4 + n _ 5 + n _ 6 , then the value of ( ∑ _ i = 1 ^ 6 n _ i ^ 2 10 ) is equal to

NTA Abhyas JEE Main 2020 Solution View → 74

If (π)/(2) < α < (3π)/(4), then 2tan ⁡ α + 1 cos^ 2 α is equal to

NTA Abhyas JEE Main 2020 Solution View → 75

If 3 + cot ⁡ 80 ^ o cot ⁡ 20 ^ o cot ⁡ 80 ^ o + cot ⁡ 20 ^ o = tan(π)/(k), then the value of k is (where, (π)/(k) is an acute angle)

NTA Abhyas JEE Main 2020 Solution View → 76

If 0 < α < (π)/(16) and ( 1 + tan ⁡ α )(1 + tan ⁡ 4α) = 2 , then the value of α is equal to

NTA Abhyas JEE Main 2020 Solution View → 77

The value of cot ⁡ 70 ^ o + 4cos ⁡ 70 ^ o is

NTA Abhyas JEE Main 2020 Solution View → 78

If ^ 6 ⁡ θ + ^ 6 ⁡ θ + k ^ 2 ⁡ 2θ = 1, then k is equal to

NTA Abhyas JEE Main 2020 Solution View → 79

The angle between the minute hand and the hour hand of a clock at “half past 3 ” is equal to

NTA Abhyas JEE Main 2020 Solution View → 80

In a triangle ABC, if sin ⁡ Acos ⁡ B = (1)/(4) and 3tan ⁡ A = tan ⁡ B, then ^ 2 ⁡ A is equal to

NTA Abhyas JEE Main 2020 Solution View → 81

The value of cos ⁡ (π)/(11)cos ⁡ (2π)/(11)cos ⁡ (3π)/(11) … … cos ⁡ (11π)/(11) is equal to

NTA Abhyas JEE Main 2020 Solution View → 82

Three positive acute angles α, β and γ satisfy the relation tan ⁡ (β)/(2) = (1)/(3)cot ⁡ (α)/(2) and cot ⁡ (γ)/(2) = (1)/(2) (3tan ⁡ (α)/(2) + cot ⁡ (α)/(2)). Then, the value of α

NTA Abhyas JEE Main 2020 Solution View → 83

If sin ⁡ 2β is the geometric mean between sin ⁡ α and cos ⁡ α, then cos ⁡ 4β is equal to

NTA Abhyas JEE Main 2020 Solution View → 84

If tan ⁡ θ = 3tan ⁡ ϕ , then the maximum value of ^ 2 ⁡ (θ -ϕ) is (where, tan ⁡ ϕ > 0)

NTA Abhyas JEE Main 2020 Solution View → 85

The value of sin ⁡ (9π)/(14)sin ⁡ (11π)/(14)sin ⁡ (13π)/(14) is equal to

NTA Abhyas JEE Main 2020 Solution View → 86

If 0 < α < (π)/(3), then α(sec ⁡ α) is

NTA Abhyas JEE Main 2020 Solution View → 87

If tan 25 ^ o = a, then the value of tan ⁡ 205 ^ o - tan ⁡ 115 ^ o tan ⁡ 245 ^ o + tan ⁡ 335 ^ o in terms of a & is

NTA Abhyas JEE Main 2020 Solution View → 88

The expression sin ⁡ 27 °cos ⁡ 57 °sin ⁡ 87 ° simplifies to

NTA Abhyas JEE Main 2020 Solution View → 89

If ((1 + cos ⁡ 2x))/(sin ⁡ 2x) + 3(1 + (tan ⁡ x)tan ⁡ (x)/(2))sin ⁡ x = 4 , then the value of tan ⁡ x can be equal to

NTA Abhyas JEE Main 2020 Solution View → 90

Let f(θ) = 1 1 + (tan ⁡ θ) ^ 2021 , then the value of &#8721; _ θ = 1 ° ^ 89 ° f (θ) & is equal to

NTA Abhyas JEE Main 2020 Solution View → 91

If x + y = 3 - cos ⁡ 4θ and x - y = 4sin ⁡ 2θ , then the value of x + y is equal to

NTA Abhyas JEE Main 2020 Solution View → 92

Let A = x ^ 4 + 4 x ^ 3 + 2 x ^ 2 - 4x + 7 where x = cot ⁡ (11π)/(8) and B = 1 - cos ⁡ 8θ ^ 2 ⁡ 4θ + 1 + cos ⁡ 8θ cot ^ 2 ⁡ 4θ where θ = 9 ^ o , then the value of (A × B)/(2) is

NTA Abhyas JEE Main 2020 Solution View → 93

The arithmetic mean of the numbers 2sin ⁡ 2 ^ o , 4sin ⁡ 4 ^ o , 6sin ⁡ 6 ^ o , … …. 178sin ⁡ 178 ^ o , 180sin ⁡ 180 ^ o is

NTA Abhyas JEE Main 2020 Solution View → 94

If sin ⁡ θ = ^ 2 ⁡ θ , then the value of ^ 12 ⁡ θ + 3 ^ 10 ⁡ θ + 3 ^ 8 ⁡ θ + ^ 6 ⁡ θ - 1 is equal to

NTA Abhyas JEE Main 2020 Solution View → 95

If cos ⁡ 2x + 2cos ⁡ x = 1, then ( ^ 2 ⁡ x)(2 - ^ 2 ⁡ x) is equal to

NTA Abhyas JEE Main 2020 Solution View → 96

If F(k) = (1 + sin(π)/(2k)) (1 + sin ⁡ (k - 1)(π)/(2k))(1 + sin ⁡ (2k + 1)(π)/(2k))(1 + sin ⁡ (3k - 1)(π)/(2k)), then the value of F (1) + F (2) + F (3) & is equal to

NTA Abhyas JEE Main 2020 Solution View → 97

Let f(x) = (sin ⁡ x + 3sin ⁡ 3x + 5sin ⁡ 5x + 3sin ⁡ 7x)/(sin ⁡ 2x + 2sin ⁡ 4x + 3sin ⁡ 6x) , wherever defined. If x _ 1 + x _ 2 = (π)/(2), where f (x) is defined at x _ 1 and x _

NTA Abhyas JEE Main 2020 Solution View → 98

For non-negative integers n, let f(n) = ∑ _ k = 0 ^ n sin ⁡ ((k + 1)/(n + 2)π)sin ⁡ ((k + 2)/(n + 2)π) ∑ _ k = 0 ^ n ^ 2 ⁡ ((k + 1)/(n + 2)π) Assuming ^ - 1 ⁡ x takes values in

JEE Advanced 2019 Solution View → 99

The value of sec ^ - 1 ⁡ ((1)/(4) ∑ _ k = 0 ^ 10 sec ⁡ ((7π)/(12) + (kπ)/(2))sec ⁡ ((7π)/(12) + ((k + 1)π)/(2))) in the interval [- (π)/(4), (3π)/(4)] equals

JEE Advanced 2019 Solution View → 100

The equation y = sinxsin ⁡ (x + 2) - ^ 2 ⁡ ( x + 1 ) represents a straight line lying in:

JEE Main 2019 Solution View → 101

The value of sin10 ° sin30 ° sin50 ° sin70 ° is:

JEE Main 2019 Solution View → 102

The value of ^ 2 10 ° – cos10 ° cos50 ° + co s ^ 2 50 ° is

JEE Main 2019 Solution View → 103

If cos(α + β) = (3)/(5), sin ⁡ ( α - β ) = (5)/(13) and 0 < α, β < (π)/(4), then tan ⁡ (2α) is equal to:

JEE Main 2019 Solution View → 104

The maximum value of 3cos ⁡ θ + 5sin ⁡ (θ - (π)/(6)) for any real value of θ is :

JEE Main 2019 Solution View → 105

Let f_ k (x)=(1)/(k)( ^ k x+ ^ k x) for k=1,2,3, … Then for all x ∈ R, the value of f_ 4 (x)-f_ 6 (x) is equal to :

JEE Main 2019 Solution View → 106

The value of cos ⁡ π 2 ^ 2 ⋅ cos ⁡ π 2 ^ 3 ⋅ … ⋅ cos ⁡ π 2 ^ 10 ⋅ sin ⁡ π 2 ^ 10 is:

JEE Main 2019 Solution View → 107

For any θ ∈ ((π)/(4), (π)/(2)), the expression 3 (sinθ - cosθ) ^ 4 + 6 (sinθ + cosθ) ^ 2 + 4 ^ 6 θ equals:

JEE Main 2019 Solution View → 108

Let a, b, c be three non-zero real numbers such that the equation 3 acos ⁡ x + 2bsin ⁡ x = c, x ∈ [- (π)/(2), (π)/(2)] has two distinct real roots α and β with α + β = (π)/(3) .

JEE Advanced 2018 Solution View → 109

The lengths of two adjacent sides of a cyclic quadrilateral are 2 units and 5 units and the angle between them is 60 ^ o . If the area of the quadrilateral is 4 3 sq. units, then

JEE Main 2017 Solution View → 110

If 5( ^ 2 ⁡ x - ^ 2 ⁡ x) = 2cos ⁡ 2x + 9, then the value of cos ⁡ 4x is

JEE Main 2017 Solution View → 111

If A > 0, B > 0 and A + B = (π)/(6) , then the minimum positive value of (tan ⁡ A + tan ⁡ B) is :

JEE Main 2016 Solution View → 112

If m and M are the minimum and the maximum values of 4 + (1)/(2) ^ 2 ⁡ 2x - 2 ^ 4 ⁡ x, x ∈ R, then M - m is equal to:

JEE Main 2016 Solution View → 113

The number of x ∈ [0, 2π] for which | 2 ^ 4 x + 18 ^ 2 x - 2 ^ 4 x + 18 ^ 2 x | = 1 is:

JEE Main 2016 Solution View → 114

In a , (a)/(b) = 2 + 3 , and ∠C = 60 ° . Then the ordered pair ( ∠A, ∠B ) is equal to:

JEE Main 2015 Solution View → 115

If cosecθ = p + q p - q (p ≠ q, p ≠ 0), then |cot((π)/(4) + (θ)/(2))| is equals to:

JEE Main 2014 Solution View → 116

Let f _ k (x) = (1)/(k)( ^ k x + ^ k x) where x ∈ R and k ≥ 1 . Then f _ 4 (x) - f _ 6 (x) equals

JEE Main 2014 Solution View → 117

The expression (tanA)/(1 - cotA) + (cotA)/(1 - tanA) can be written as :

JEE Main 2013 Solution View → 118

Let f:(-1,1) arrow I R be such that f( 4 θ)= 2 2- ^ 2 θ for θ ∈(0, (π)/(4)) ∪((π)/(4), (π)/(2)) . Then the value (s) of f((1)/(3)) is (are)

JEE Advanced 2012 Solution View → 119

The value of 255^ ∘ + 195^ ∘ is

JEE Main 2012 Solution View → 120

Suppose θ and φ(≠ 0) are such that (θ+φ) , sec θ and (θ-φ) are in A.P. If θ=k ((φ)/(2)) for some k , then k is equal to

JEE Main 2012 Solution View → 121

Let (α+β)=(4)/(5) and let (α-β)=(5)/(13) , where 0 ≤ α, β ≤ (π)/(4) , then 2 α=

JEE Main 2010 Solution View → 122

Let θ ∈(0, (π)/(4)) and t_1=( θ)^ θ , t_2=( θ)^ θ and t_4=( θ)^ θ , then

JEE Advanced 2006 Solution View → 123

Let α, β be such that π < α-β < 3 π . If α+ β=-(21)/(65) and α+ β=-(27)/(65) , then the value of (α-β)/(2) is

JEE Main 2004 Solution View → 124

The period of ^2 θ is

JEE Main 2002 Solution View → 125

The number of solutions of equation, sin5xcos3x = sin6xcos2x ,~in the interval [0, π] are

Highly selective Backlog Qs for JEE Main Solution View → 126

If x ^ 3 θ+y ^ 3 θ= θ θ and x θ=y θ, then x^ 2 +y^ 2 =

Highly selective Backlog Qs for JEE Main Solution View → 127

If (x-y), x, (x+y) are three distinct numbers which are in harmonic progression and x ≠ y , then 1+ y is equal to

Highly selective Backlog Qs for JEE Main Solution View → 128

The sum of all the solution of the equation θ ((π)/(3)+θ) ((π)/(3)-θ)=(1)/(4), θ ∈[0,6 π]

Highly selective Backlog Qs for JEE Main Solution View → 129

The value of (2 π)/(15) (4 π)/(15) (8 π)/(15) (14 π)/(15) is :

Highly selective Backlog Qs for JEE Main Solution View → 130

If θ+ (θ+(π)/(3))+ (θ+(2 π)/(3))=3 , then which of the following is equal to 1 ?

Highly selective Backlog Qs for JEE Main Solution View → 131

What is the minimum value of θ+ 2 θ ?

Highly selective Backlog Qs for JEE Main Solution View → 132

The number of x ∈ [ 0, 2 π] for which | 2 ^ 4 x + 18 ^ 2 x - 2 ^ 4 x + 18 ^ 2 x | = 1 is:

Highly selective Backlog Qs for JEE Main Solution View → 133

A 2 A 4 A … 2^ n-1 A equals

Highly selective Backlog Qs for JEE Main Solution View → 134

The solution set of (5+4 θ)(2 θ+1)=0 in the interval [0,2 π] , is :

Highly selective Backlog Qs for JEE Main Solution View → 135

The value of tan 9 ^ ^ o - tan 27 ^ ^ o - tan 63 ^ ^ o + tan 81 ^ ^ o is _____.

Highly selective Backlog Qs for JEE Main Solution View → 136

The general solution of |sin ⁡ x| = cos ⁡ x is (when n ∈ I ) given by

Highly selective Backlog Qs for JEE Main Solution View → 137

Let (α+β)=(4)/(5) and let (α-β)=(5)/(13) , where 0 ≤ α, β ≤ (π)/(4) , then 2 α=

Highly selective Backlog Qs for JEE Main Solution View → 138

The value of cos ⁡ π 2 ^ 2 ⋅ cos ⁡ π 2 ^ 3 ⋅ … ⋅ cos ⁡ π 2 ^ 10 ⋅ sin ⁡ π 2 ^ 10 is:

Highly selective Backlog Qs for JEE Main Solution View → 139

If A=35^ ^ ^ ∘ , B=15^ ^ ^ ∘ and C=40^ ^ ^ ∘ , then A · B+ B · C+ C · A is equal to

Highly selective Backlog Qs for JEE Main Solution View → 140

The value of 36 (4 ^ 2 9 ^ ∘ - 1) ( 4 ^ 2 27 ^ ∘ - 1\ right)( 4 ^ 2 81 ^ ∘ - 1\ right)(4 ^ 2 243 ^ ∘ - 1) is

Highly selective Backlog Qs for JEE Main Solution View → 141

The value of cos ((2π)/(7)) +cos ((4π)/(7)) ++cos((6π)/(7))is equal to

Highly selective Backlog Qs for JEE Main Solution View → 142

If 0 < α < (π)/(3), then α ( sec ⁡ α)is

Highly selective Backlog Qs for JEE Main Solution View → 143

If tanA = 1 x(x^ 2 + x + 1) , tanB = x x^ 2 + x + 1 and tanC = (x^ - 3 + x^ - 2 + x^ - 1 )(1)/(2), 0 < A, B, C < (π)/(2) , then A + B is equal to:

Highly selective Backlog Qs for JEE Main Solution View → 144

Let S = \ θ ∈ (0, (π)/(2)): ∑ _ m = 1 ^ 9 sec(θ + (m - 1)(π)/(6))sec(θ + (mπ)/(6)) = - (8)/(3)\ . Then

Highly selective Backlog Qs for JEE Main Solution View → 145

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

99 Percentile Qs Bank for JEE Main Solution View → 146

The value of 18^ ^ ^ ∘ is

99 Percentile Qs Bank for JEE Main Solution View → 147

The value of(1 + cos(π)/(8)) ( 1 + cos(3π)/(8))( 1 + cos(5π)/(8)) (1 + cos(7π)/(8))is equal to

99 Percentile Qs Bank for JEE Main Solution View → 148

If (y+z-x), (z+x-y) and (x+y-z) are in A.P., then

99 Percentile Qs Bank for JEE Main Solution View → 149

If the value of (1 + tan 1 ^ o )(1 + tan 2 ^ o )(1 + tan 3 ^ o )… … … . ( 1 + tan 44 ^ o ) ( 1 + tan 45 ^ o ) is 2 ^ λ , then the sum of the digits of the number λ is

99 Percentile Qs Bank for JEE Main Solution View → 150

12^ ^ ^ ∘ - 12^ ^ ^ ∘ 12^ ^ ^ ∘ + 12^ ^ ^ ∘ + 147^ ^ ^ ∘ 147^ ^ ^ ∘ =

99 Percentile Qs Bank for JEE Main Solution View → 151

If a ^ 2 ⁡ x + b ^ 2 ⁡ x = c, b ^ 2 ⁡ y + a ^ 2 ⁡ y = d and atan ⁡ x = btan ⁡ y, then a^ 2 b^ 2 is equal to (Here a, b, c and d are distinct)

99 Percentile Qs Bank for JEE Main Solution View → 152

The value of the expression (2 ( sin1 ° + sin2 ° + sin3 ° + . . . . . . . . + sin89 ° ))/(2 ( cos1 ° + cos2 ° + cos3 ° + . . . . . . . . + cos44 ° ) + 1) is equal to

99 Percentile Qs Bank for JEE Main Solution View → 153

Let f(x) = max\ tan ⁡ x,cot ⁡ x\ . Then the number of roots of the equation f ( x) = (1)/(2)in ( 0, 2π)is

99 Percentile Qs Bank for JEE Main Solution View → 154

If E = ^ 2 ⁡ 71 ^ o + ^ 2 ⁡ 49 ^ o + cos ⁡ 71 ^ o cos ⁡ 49 ^ o , then the value of 10E is equal to

99 Percentile Qs Bank for JEE Main Solution View → 155

The solution set of (5+4 θ)(2 θ+1)=0 in the interval [0,2 π] , is :

99 Percentile Qs Bank for JEE Main Solution View → 156

1 - 2[cos 60 ^ o - cos 80 ^ o ] 2sin 10 ^ o = ….

99 Percentile Qs Bank for JEE Main Solution View → 157

sin ⁡ [3 ^ - 1 (0.4)] = ….

99 Percentile Qs Bank for JEE Main Solution View → 158

Consider the function defined by f(x) = sin ⁡ x 1 + ^ 2 ⁡ x + cos ⁡ x 1 + ^ 2 ⁡ x for permissible values. Then which of the following is true?

99 Percentile Qs Bank for JEE Main Solution View → 159

A+2 2 A+4 4 A+8 Cot 8 A=

99 Percentile Qs Bank for JEE Main Solution View → 160

If x= 15^ ^ ^ ∘ , y=cosec 75^ ^ ^ ∘ and z=4 18^ ^ ^ ∘ , then :

99 Percentile Qs Bank for JEE Main Solution View → 161

If A=35^ ^ ^ ∘ , B=15^ ^ ^ ∘ and C=40^ ^ ^ ∘ , then A · B+ B · C+ C · A is equal to

99 Percentile Qs Bank for JEE Main Solution View → 162

In a triangle ABC , with usual notations, if c=4 , then value of (a-b)^2 ^2 (C)/(2)+(a+b)^2 ^2 (C)/(2) is

99 Percentile Qs Bank for JEE Main Solution View → 163

If θ+ (θ+(π)/(3))+ (θ+(2 π)/(3))=3 , then which of the following is equal to 1 ?

99 Percentile Qs Bank for JEE Main Solution View → 164

The maximum value of the function y=e^ 5+ 3 x+ x is

99 Percentile Qs Bank for JEE Main Solution View → 165

A 2 A 4 A … 2^ n-1 A equals

99 Percentile Qs Bank for JEE Main Solution View → 166

( x)/( (x-2 y))=λ ⇒ (x-y) y is equal to

99 Percentile Qs Bank for JEE Main Solution View → 167

The number of solutions in [0,2 π] of the equation 16^ ^2 x +16^ ^2 x =10 is

99 Percentile Qs Bank for JEE Main Solution View → 168

81^ ^ ^ ∘ - 63^ ^ ^ ∘ - 27^ ^ ^ ∘ + 9^ ^ ^ ∘ equals to

99 Percentile Qs Bank for JEE Main Solution View → 169

If sin( &#952; _ 1 ) + sin( &#952; _ 2 ) + . . . . . . + sin( &#952; _ n ) = n . Then value of sin( &#952; _ 1 ) + cos( &#952; _ 2 ) + sin( &#952; _ 3 ) + cos ( &#952; _ 4 ) . . .

99 Percentile Qs Bank for JEE Main Solution View → 170

If θ+φ=α and θ=k φ (where K>1) , then the value of (θ-φ) is

99 Percentile Qs Bank for JEE Main Solution View → 171

The sum of the solutions in (0,2 π) the equation x ((π)/(3)-x) ((π)/(3)+x)=(1)/(4) is

99 Percentile Qs Bank for JEE Main Solution View → 172

^2 76^ ^ ^ ∘ + ^2 16^ ^ ^ ∘ - 76^ ^ ^ ∘ 16^ ^ ^ ∘ is equal to

99 Percentile Qs Bank for JEE Main Solution View → 173

If A=(7)/(25) and (3 π)/(2) < A < 2 π , then (A)/(4)+ (A)/(2)- 2 A=

99 Percentile Qs Bank for JEE Main Solution View → 174

If α = 2 6^∘ + 126^∘ 3 , then which of the following quadratic equations has α as one of its roots?

JEE Main Solution View → 175

Let S = ∑_ k=1 ^ 5 ^2 ( (kπ)/(11) ) and P = ∏_ k=1 ^ 5 ( (kπ)/(11) ) . The value of the ratio (S)/(P) is equal to:

JEE Main Solution View → 176

In a triangle ABC , the tangents of angles A and B are given by A = x and B = (x^2+1)/(2x) , where x > 1 . If C = (13)/(6) , then the value of x is:

JEE Main Solution View → 177

Let x, y ∈ (0, (π)/(2)) be such that (x+y) = 2 (x-y) and 5 (x+y) = 3 (x-y) . Then the value of ^2 x is equal to

JEE Main Solution View → 178

Let S_n = ∑_ k=1 ^ n (((2k-1)π)/(12)) (((2k+1)π)/(12)) . If S_n = 2 3 - 6 , then the sum of the first three positive integer values of n for which this holds is

JEE Main Solution View → 179

If cosec θ - 3 θ = 4 and θ ∈ (0, (π)/(2)) , then the value of θ is :

JEE Main Solution View → 180

If ( (x+y))/( (x-y)) = (a+b)/(a-b) , where a, b ≠ 0 and x, y are such that x and y are well-defined and non-zero, then which of the following relations is true?

JEE Main Solution View → 181

The value of the expression 3 20^ ∘ - 4 20^ ∘ is equal to :

JEE Main Solution View → 182

If (α+β) = (3)/(5) and α = (5)/(13) , where α+β lies in the IV^ th quadrant and α lies in the II^ nd quadrant, then the value of β and the quadrant in which β lies, respectively

JEE Main Solution View → 183

Let A and B be acute angles measured counterclockwise from the positive x -axis. If the point P(2x+1, 1) lies on the terminal side of angle A and the point Q(x+1, x) lies on the

JEE Main Solution View → 184

Let S = ∑_ r=1 ^ 3 cosec((π)/(8) + (r-1)(π)/(4)) cosec((π)/(8) + r(π)/(4)) . If S = a + b 2 where a and b are rational numbers, then the quadratic equation whose roots are (a+b)

JEE Main Solution View → 185

Let S = \ θ ∈ (0, (π)/(2)) : ∑_ m=1 ^ 6 (θ + (m-1)(π)/(4)) (θ + (mπ)/(4)) = 4 2 \ . If α and β are the largest and smallest elements of S respectively, then the value of α - β is

JEE Main Solution View → 186

The value of (2 12^∘ + 108^∘)^2 + (2 12^∘ - 18^∘)^2 is

JEE Main Solution View → 187

Let a function f(x) be defined as f(x) = ∑_ k=1 ^ 8 cosec((kπ)/(3) + x) cosec(((k+1)π)/(3) + x) . The value of |f((π)/(12))| is equal to :

JEE Main Solution View → 188

Two straight lines L_1 and L_2 have slopes -2 and 3 , respectively. Let θ and φ be their respective angles of inclination. The value of (θ+φ) and the quadrant in which θ+φ lies

JEE Main Solution View → 189

Let P_n = ∏_ k=0 ^ n-1 ( (2^k π)/(129) ) . If P_n = (1)/(2^n) , then the smallest positive integer n that satisfies this equation is:

JEE Main Solution View →
Practice all Trigonometric Ratios & Identities questions in the app →

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 Ratios & Identities in other exams

NDA Trigonometric Ratios & Identities (295)BITSAT Trigonometric Ratios & Identities (16)