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JEE • MATHEMATICS • TRIGONOMETRIC EQUATIONS

Trigonometric equations practice · Easy

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 241-261 of 261 questions
241 Easy
241 of 261
Application +4 | -1
The value of expression 1−4sin⁡10∘sin⁡70∘2sin⁡10∘\frac{1-4 \sin 10^{\circ} \sin 70^{\circ}}{2 \sin 10^{\circ}} is
View answer and explanation
Correct option: B
1
Option B (1) is correct because using the product-to-sum trigonometric identity, the expression simplifies to 1.
242 Easy
242 of 261
Analyzing +4 | -1
If y=sin⁡  3θsin⁡  θ,   θ≠n  πy = \frac{{\sin \,\,3\theta }}{{\sin \,\,\theta }},\;\,\theta \ne n\;\pi, then

View answer and explanation
Correct option: D
y∈[−1,   3)y \in \left[ { - 1,\,\;3} \right)
Option D (y∈[−1,  3)y \in \left[ { - 1,\;3} \right)) is correct because it represents the range of the function y=sin⁡ 3θsin⁡ θy = \frac{{\sin \,3\theta }}{{\sin \,\theta }} for θ≠n  π\theta \ne n\;\pi.
243 Easy
243 of 261
Analyzing +4 | -1
Total number of solutions ofsin⁡4x+cos⁡4x=sin⁡x  ⋅  cos⁡x   in   [0,   2π]{\sin ^4}x + {\cos ^4}x = \sin x\,\, \cdot \,\,\cos x\,\;\mathrm{in}\,\;\left[ {0,\;\,2\pi } \right] is equal to
View answer and explanation
Correct option: A
2
Option A (2) is correct because by simplifying the given equation, we find that there are only two solutions for x in the interval [0, 2π\pi].
244 Easy
244 of 261
Application +4 | -1
If 1+sin⁡θ+sin⁡2θ+……∞=4+23,0<θ<π,θ≠π21+\sin \theta+\sin ^2 \theta+\ldots \ldots \infty=4+2 \sqrt{3}, 0<\theta<\pi, \theta \neq \frac{\pi}{2}, then
View answer and explanation
Correct option: D
θ=π3\theta=\frac{\pi}{3} or 2π3\frac{2 \pi}{3}
Option D (θ=π3\theta = \frac{\pi}{3} or 2π3\frac{2\pi}{3}) is correct because it is the solution obtained by using the formula for the sum of an infinite geometric series and solving for sin⁡θ\sin \theta.
245 Easy
245 of 261
Application +4 | -1
The solution set of the inequality 3(2−x)≥2(1−x)3(2-x) \geq 2(1-x) is (−∞,a](-\infty, a]. The value of aa is
View answer and explanation
Correct option: A
4
Option A (4) is correct because solving the inequality 3(2−x)≥2(1−x)3(2-x) \geq 2(1-x) results in x≤4x \leq 4, which corresponds to the interval (−∞,4](-\infty, 4].
246 Easy
246 of 261
Application +4 | -1
Find the general solution of the equation sin⁡x−3sin⁡2x+sin⁡3x=cos⁡x−3cos⁡2x+cos⁡3x\sin x-3 \sin 2 x+\sin 3 x=\cos x-3 \cos 2 x+\cos 3 x
View answer and explanation
Correct option: C
nπ2+π8\frac{n \pi}{2}+\frac{\pi}{8}
Option C (nπ2+π8\frac{{n \pi}}{{2}}+\frac{{\pi}}{{8}}) is the correct general solution obtained by simplifying the given trigonometric equation and solving for x.
247 Easy
247 of 261
Application +4 | -1
The solution of the equation tan⁡θtan⁡2θ=1\tan \theta \tan 2 \theta=1 is
View answer and explanation
Correct option: D
nπ±π6n \pi \pm \frac{\pi}{6}
Option D (nπ±π6n \pi \pm \frac{{\pi}}{{6}}) is correct because it represents the general solution derived from solving the trigonometric equation tan⁡θtan⁡2θ=1\tan \theta \tan 2 \theta = 1.
248 Easy
248 of 261
Application +4 | -1
For m≠nm \ne n, if tan⁡  m  θ=tan⁡  n  θ\tan \,\,m\;\theta = \tan \,\,n\;\theta, the different values of θ\theta are in
View answer and explanation
Correct option: A
A.P.
Option A (A.P.) is the correct answer because the values of θ\theta form an arithmetic progression.
249 Easy
249 of 261
Analyzing +4 | -1
If x  cos⁡  θ=y  cos⁡(θ+2π3)=z  cos⁡(θ+4π3)x\,\,\cos \,\,\theta = y\,\,\cos \left( {\theta + \frac{{2\pi }}{3}} \right) = z\,\,\cos \left( {\theta + \frac{{4\pi }}{3}} \right), then the value of 1x+1y+1z\frac{1}{x} + \frac{1}{y} + \frac{1}{z} is equal to
View answer and explanation
Correct option: C
0
Option C (0) is correct because the sum of cosines with angles in arithmetic progression is zero when the common difference is 2π3\frac{{2\pi}}{3}.
250 Easy
250 of 261
Understanding +4 | -1
Which of the following is not correct?
View answer and explanation
Correct option: C
sec⁡θ=12\sec \theta=\frac{1}{2}
Option C (sec⁡θ=12\sec \theta=\frac{1}{2}) is correct because the range of the secant function is (−∞,−1]∪[1,∞)(-\infty, -1] \cup [1, \infty), so it cannot be between -1 and 1.
251 Easy
251 of 261
Application +4 | -1
If cos⁡  3  x+sin⁡(2c−7  π6)=−2\cos \,\,3\;x + \sin \left( {2c - \frac{{7\;\pi }}{6}} \right) = - 2 then x=x =
View answer and explanation
Correct option: A
π3  (6k+1),  k∈Z\frac{\pi }{3}\,\,\left( {6k + 1} \right),\,\,k \in Z
Option A is correct because it provides the general solution for x that satisfies the given trigonometric equation.
252 Easy
252 of 261
Analyzing +4 | -1
If x,y∈[0,2π]x, y \in[0,2 \pi], then total number of ordered pairs (x,y)(x, y) satisfying sin⁡xcos⁡y=1\sin x \cos y=1 is
View answer and explanation
Correct option: B
3
Option B (3) is correct because there are three ordered pairs (x, y) that satisfy the given equation sin(x)cos(y) = 1 within the specified interval.
253 Easy
253 of 261
Application +4 | -1
The numerical value of tan⁡π3+2tan⁡2π3+4tan⁡4π3+8tan⁡8π3\tan \frac{\pi}{3}+2 \tan \frac{2 \pi}{3}+4 \tan \frac{4 \pi}{3}+8 \tan \frac{8 \pi}{3} is
View answer and explanation
Correct option: A
−53-5 \sqrt{3}
Option A (−53-5 \sqrt{3}) is correct because using the properties of the tangent function, the expression simplifies to −5tan⁡π3-5 \tan \frac{\pi}{3}, which equals −53-5\sqrt{3}.
254 Easy
254 of 261
Analyzing +4 | -1
The number of solutions of the equation tan⁡  x+sec⁡  x=2  cos⁡  x\tan \,\,x + \sec \,\,x = 2\,\,\cos \,\,x lying in the interval [0,   2  π]\left[ {0,\,\;2\;\pi } \right] is

View answer and explanation
Correct option: C
2\mathrm{2}
Option C (2) is correct because the equation tan⁡x+sec⁡x=2cos⁡x\tan x + \sec x = 2 \cos x has two solutions in the interval [0,2π][0, 2\pi].
255 Easy
255 of 261
Application +4 | -1
If θ∈[0,2π]\theta \in[0,2 \pi] then number of ordererd pairs (x,θ)(x, \theta) which satisfies x4−2x2cos⁡θ+1=0x^4-2 x^2 \cos \theta+1=0 is/are
View answer and explanation
Correct option: D
4
Option D (4) is correct because the equation can be simplified to find the possible values of x and theta that satisfy it.

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SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs
256 Easy
256 of 261
Analyzing +4 | -1
The value(s) of x∈[−2π,2π]x \in[-2 \pi, 2 \pi] such that sin⁡x+icos⁡x1+i,i=−1\frac{\sin x+i \cos x}{1+i}, i=\sqrt{-1} is purely imaginary, is/are given by
View answer and explanation
Correct option: A
nπ−π4n \pi-\frac{\pi}{4}
Option A (nπ−π4n \pi - \frac{\pi}{4}) is correct because it satisfies the condition where the real part of the given expression is zero, making it purely imaginary.
257 Easy
257 of 261
Application +4 | -1
If cos⁡  θ+cos⁡  2θ+cos⁡  3θ=0\cos \,\,\theta + \cos \,\,2\theta + \cos \,\,3\theta = 0, the general value of θ\theta is
View answer and explanation
Correct option: D
θ=2nπ  ±  2 π3\theta = 2n\pi \,\, \pm \,\,\frac{{2\,\pi }}{3}
Option D (θ=2nπ ± 2 π3\theta = 2n\pi \, \pm \, \frac{{2\,\pi }}{3}) is correct because solving the trigonometric equation cos⁡θ+cos⁡2θ+cos⁡3θ=0\cos \theta + \cos 2\theta + \cos 3\theta = 0 leads to the general solution θ=2nπ±2π3\theta = 2n\pi \pm \frac{2\pi}{3}.
258 Easy
258 of 261
Analyzing +4 | -1
The most general solutions of the equation sec⁡x−1=(2−1)tan⁡x\sec x - 1 = \left( {\sqrt 2 - 1} \right)\tan x are given by
View answer and explanation
Correct option: B
2nπ,   2nπ+π42n\pi ,\,\;2n\pi + \frac{\pi }{4}
Option B (2nπ,  2nπ+π42n\pi ,\;2n\pi + \frac{\pi }{4}) is correct because these are the general solutions obtained by solving the given trigonometric equation.
259 Easy
259 of 261
Application +4 | -1
{x∈R:cos⁡  2x+2cos⁡2x=2}\left\{ {x \in R:\cos \,\,2x + 2{{\cos }^2}x = 2} \right\} is equal to
View answer and explanation
Correct option: B
{nπ±π6  :  n∈Z}\left\{ {n\pi \pm \frac{\pi }{6}\,\,:\,\,n \in Z} \right\}
Option B ({nπ±π6  :  n∈Z}\left\{ {n\pi \pm \frac{\pi }{6}\,\,:\,\,n \in Z} \right\}) is correct because it represents the general solution of the given trigonometric equation.
260 Easy
260 of 261
Analyzing +4 | -1
The number of solutions of the given equation tan⁡θ+sec⁡θ=3\tan \mathrm{\theta } + \sec \mathrm{\theta } = \sqrt 3, where 0<θ<2π0 < \mathrm{\theta } < 2\mathrm{\pi } is
View answer and explanation
Correct option: C
2
Option C (2) is correct because solving the trigonometric equation tan⁡θ+sec⁡θ=3\tan \theta + \sec \theta = \sqrt 3 in the interval 0<θ<2π0 < \theta < 2\pi yields two solutions.
261 Easy
261 of 261
Application +4 | -1
The general solution of the trigonometric equation tan⁡θ=cot⁡α\tan \theta=\cot \alpha is
View answer and explanation
Correct option: A
θ=nπ+π2−α\theta=n \pi+\frac{\pi}{2}-\alpha
Option A (θ=nπ+π2−α\theta=n \pi+\frac{{\pi}}{{2}}-\alpha) is correct because it represents the general solution derived from the given equation tan⁡θ=cot⁡α\tan \theta = \cot \alpha using trigonometric identities.
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