Quantrex Academy
JEE · NEET · NDA PYQs with solutions
Open app
Home
·
NTA Abhyas JEE Main
·
Mathematics
·
Trigonometric Equations
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Trigonometric Equations
NTA Abhyas 2020 · Mathematics · Trigonometric Equations
General solution of the equation 4 2θ + ^ 2 θ = ^ 2 θ is (where, n...
General solution of the equation
4
cot
2
θ
+
tan
2
θ
=
cot
2
θ
4\cot 2\theta + \tan^{2}\theta = \cot^{2} \theta
4
cot
2
θ
+
tan
2
θ
=
cot
2
θ
is (where,
n
∈
Z
n \in \mathbb{Z}
n
∈
Z
)
Options
A
n
π
±
π
4
n\pi \pm \dfrac{\pi}{4}
nπ
±
4
π
B
n
π
±
π
3
n\pi \pm \dfrac{\pi}{3}
nπ
±
3
π
C
2
n
π
±
π
3
2n\pi \pm \dfrac{\pi}{3}
2
nπ
±
3
π
D
2
n
π
±
π
6
2n\pi \pm \dfrac{\pi}{6}
2
nπ
±
6
π
Correct answer
A.
n
π
±
π
4
n\pi \pm \dfrac{\pi}{4}
nπ
±
4
π
Step-by-step solution
The given equation can be written as
2
(
1
−
tan
2
θ
)
t
a
n
θ
+
tan
2
θ
=
1
tan
2
θ
\dfrac{2\left(1 - \tan^{2}\theta\right)}{tan \theta} + \tan^{2}\theta = \dfrac{1}{\tan^{2}\theta}
t
an
θ
2
(
1
−
tan
2
θ
)
+
tan
2
θ
=
tan
2
θ
1
⇒
2
(
1
−
tan
2
θ
)
+
tan
3
θ
t
a
n
θ
=
1
tan
2
θ
⇒ \dfrac{2\left(1 - \tan^{2}\theta\right) + \tan^{3}\theta}{tan \theta} = \dfrac{1}{\tan^{2}\theta}
⇒
t
an
θ
2
(
1
−
tan
2
θ
)
+
tan
3
θ
=
tan
2
θ
1
⇒
2
(
1
−
tan
2
θ
)
t
a
n
θ
+
tan
4
θ
−
1
=
0
⇒ 2\left(1 - \tan^{2}\theta\right)tan \theta + \tan^{4}\theta - 1 = 0
⇒
2
(
1
−
tan
2
θ
)
t
an
θ
+
tan
4
θ
−
1
=
0
⇒
(
1
−
tan
2
θ
)
(
2
t
a
n
θ
−
1
−
tan
2
θ
)
=
0
⇒ \left(1 - \tan^{2}\theta\right)\left(2tan \theta - 1 - \tan^{2}\theta\right) = 0
⇒
(
1
−
tan
2
θ
)
(
2
t
an
θ
−
1
−
tan
2
θ
)
=
0
⇒
(
1
−
tan
2
θ
)
(
1
−
t
a
n
θ
)
2
=
0
⇒ \left(1 - \tan^{2}\theta\right){\left(1 - tan \theta\right)}^{2} = 0
⇒
(
1
−
tan
2
θ
)
(
1
−
t
an
θ
)
2
=
0
⇒
(
1
+
t
a
n
θ
)
(
1
−
t
a
n
θ
)
3
=
0
⇒ \left(1 + tan \theta\right)\left(1 - tan \theta\right)3 = 0
⇒
(
1
+
t
an
θ
)
(
1
−
t
an
θ
)
3
=
0
⇒
t
a
n
θ
=
±
1
⇒ tan \theta = \pm 1
⇒
t
an
θ
=
±
1
θ
=
n
π
±
π
4
\theta = n\pi \pm \dfrac{\pi}{4}
θ
=
nπ
±
4
π
Practice Trigonometric Equations on Quantrex Academy →
← Previous question
If ^ 2 (x + y) + ^ 2 (x + y) = 1 - 2x - x^ 2 , then (where, n ∈ ℤ)
Next question →
The number of solutions in the interval [0, π] of the equation sin ^ 3 xcos 3x + sin…
More from Trigonometric Equations
Match each entry in List-I to the correct entry in List-II and choose the correct option.…
JEE Advanced 2026
Passage: Consider the curve C_1 given by y = e^ -x for x ∈ [0, 10π] , and the curve C_2…
JEE Advanced 2026
Let S = \ θ ∈ (-2π, 2π) : θ + 1 = 3 θ\ . Then ∑_ θ ∈ S θ is equal to:
JEE Main 2026
If S = \ θ ∈ [-π, π] : θ (5θ)/(2) = 7θ (7θ)/(2)\ , then n(S) is equal to _______.
JEE Main 2026
Let S = \ x ∈ [-π, π] : x ( x + x) = a, a ∈ ℤ\ . Then n(S) is equal to :
JEE Main 2026
The number of elements in the set \ x ∈[0,180^ ∘ ]: (x+100^ ∘ )= (x+50^ ∘ ) x (x-50^ ∘ )\…
JEE Main 2026
Number of solutions of 3 2 θ+8 θ+3 3 =0, θ ∈[-3 π, 2 π] is:
JEE Main 2026
The number of solutions of the equation 2 θ (θ)/(2)+ (5 θ)/(2)=2 ^3 (5 θ)/(2) in…
JEE Main 2025
If for θ ∈[-(π)/(3), 0] , the points (x, y)=(3 (θ+(π)/(3)), 2 (θ+(π)/(6))) lie on x y+α…
JEE Main 2025
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
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
The number of solutions of the equation 2 x+3 x=π, x ∈[-2 π, 2 π]-\ ± (π)/(2), ± (3…
JEE Main 2025
If θ ∈[-(7 π)/(6), (4 π)/(3)] , then the number of solutions of 3 cosec^2 θ-2( 3 -1)…
JEE Main 2025
If θ ∈[-2 π, 2 π] , then the number of solutions of 2 2 ^2 θ+(2- 6 ) θ- 3 =0 , is equal…
JEE Main 2025
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
Let f: ℝ arrow ℝ be a function defined by f(x)=\ array cc x^2 ((π)/(x^2)), & if x ≠ 0 0…
JEE Advanced 2024
Full Trigonometric Equations list
Trigonometric Equations JEE Maths PYQs
JEE Mathematics PYQs
All NTA Abhyas JEE Main PYQs
