If $\sin \theta=\sin \alpha$, then

$\frac{\theta+\alpha}{2}$ is any odd multiple of $\pi$ and $\frac{\theta-\alpha}{2}$ is any multiple of $\pi$

$\frac{\theta+\alpha}{2}$ is any multiple of $\frac{\pi}{2}$ and $\frac{\theta-\alpha}{2}$ is any even multiple of $\pi$

$\frac{\theta+\alpha}{2}$ is any even multiple of $\frac{\pi}{2}$ and $\frac{\theta-\alpha}{2}$ is any odd multiple of $\pi$

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JEE • MATHEMATICS • TRIGONOMETRIC EQUATIONS

Trigonometric equations practice · Mixed difficulty

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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 571-581 of 581 questions

571 Easy

571 of 581

Application +4 | -1

\cos \,\,\theta + \cos \,\,2\theta + \cos \,\,3\theta = 0

, the general value of

\theta

View answer and explanation

Correct option: D

\theta = 2n\pi \,\, \pm \,\,\frac{{2\,\pi }}{3}

Option D (

\theta = 2n\pi \, \pm \, \frac{{2\,\pi }}{3}

) is correct because solving the trigonometric equation

\cos \theta + \cos 2\theta + \cos 3\theta = 0

leads to the general solution

\theta = 2n\pi \pm \frac{2\pi}{3}

572 Easy

572 of 581

Analyzing +4 | -1

The most general solutions of the equation

\sec x - 1 = \left( {\sqrt 2 - 1} \right)\tan x

are given by

View answer and explanation

Correct option: B

2n\pi ,\,\;2n\pi + \frac{\pi }{4}

Option B (

2n\pi ,\;2n\pi + \frac{\pi }{4}

) is correct because these are the general solutions obtained by solving the given trigonometric equation.

573 Easy

573 of 581

Application +4 | -1

\left\{ {x \in R:\cos \,\,2x + 2{{\cos }^2}x = 2} \right\}

is equal to

View answer and explanation

Correct option: B

\left\{ {n\pi \pm \frac{\pi }{6}\,\,:\,\,n \in Z} \right\}

Option B (

\left\{ {n\pi \pm \frac{\pi }{6}\,\,:\,\,n \in Z} \right\}

) is correct because it represents the general solution of the given trigonometric equation.

574 Medium

574 of 581

Application +4 | -1

|\tan x| \leq 1

and

x \in[-\pi, \pi]

, then the solution set for

x

is:

View answer and explanation

Correct option: A

\left[-\pi,-\frac{3 \pi}{4}\right] \cup\left[-\frac{\pi}{4}, \frac{\pi}{4}\right] \cup\left[\frac{3 \pi}{4}, \pi\right]

Option A is correct because it represents the intervals where the absolute value of the tangent function is less than or equal to 1 within the given range of

[-\pi, \pi]

575 Medium

575 of 581

Application +4 | -1

If the equation

4 \cos ^2 x \sin x-2 \sin ^2 x=3 \sin x

, then

x

is equal to-

View answer and explanation

Correct option: B

n \pi+(-1)^{n+1}\left(\frac{3 \pi}{10}\right)

Option B (

n \pi+(-1)^{{n+1}}(\frac{{3 \pi}}{{10}})

) is correct because it represents the general solution of the given trigonometric equation, derived by factoring and solving for x.

576 Easy

576 of 581

Analyzing +4 | -1

The number of solutions of the given equation

\tan \mathrm{\theta } + \sec \mathrm{\theta } = \sqrt 3

, where

0 < \mathrm{\theta } < 2\mathrm{\pi }

View answer and explanation

Correct option: C

Option C (2) is correct because solving the trigonometric equation

\tan \theta + \sec \theta = \sqrt 3

in the interval

0 < \theta < 2\pi

yields two solutions.

577 Medium

577 of 581

Analyzing +4 | -1

\sin \theta=\sin \alpha

, then

View answer and explanation

Correct option: A

\frac{\theta+\alpha}{2}

is any odd multiple of

\frac{\pi}{2}

and

\frac{\theta-\alpha}{2}

is any multiple of

\pi

Option A (

\frac{\theta+\alpha}{2}

is any odd multiple of

\frac{\pi}{2}

and

\frac{\theta-\alpha}{2}

is any multiple of

\pi

) is correct because it represents the general solution for the given trigonometric equation.

578 Medium

578 of 581

Application +4 | -1

\cos x \cos 2 x \cos 4 x \cos 8 x=\frac{\operatorname{cosec} x}{16}

then-

View answer and explanation

Correct option: A

x=(4 n+1) \frac{\pi}{32}

Option A (

x=(4 n+1) \frac{\pi}{32}

) is correct because it represents the solution obtained after repeatedly applying the identity 2sin(x)cos(x) = sin(2x) and solving the resulting equation.

579 Easy

579 of 581

Application +4 | -1

The general solution of the trigonometric equation

\tan \theta=\cot \alpha

View answer and explanation

Correct option: A

\theta=n \pi+\frac{\pi}{2}-\alpha

Option A (

\theta=n \pi+\frac{{\pi}}{{2}}-\alpha

) is correct because it represents the general solution derived from the given equation

\tan \theta = \cot \alpha

using trigonometric identities.

580 Medium

580 of 581

Application +4 | -1

The general solution of the equation

\tan 2\theta \,.\,\,\tan \theta = 1

for

n \in Z

View answer and explanation

Correct option: B

\left( {2n + 1} \right)\frac{\pi }{6}

Option B (

\left( {2n + 1} \right)\frac{\pi }{6}

) is correct because it represents the general solution derived from the given trigonometric equation after simplification.

581 Medium

581 of 581

Application +4 | -1

\tan \alpha=\frac{1}{7}

and

\sin \beta=\frac{1}{\sqrt{10}}

, where

0 < \alpha, \beta < \frac{\pi}{2}

, then

2 \beta

is equal to

View answer and explanation

Correct option: A

\frac{\pi}{4}-\alpha

Option A (

\frac{{\pi}}{{4}} - \alpha

) is correct because by calculating

\sin 2\beta

and then

\tan(\alpha + 2\beta)

, we find that

\alpha + 2\beta = \frac{{\pi}}{{4}}

Revision notes and key takeaways

Review TRIGONOMETRIC EQUATIONS in your textbook or class notes, then use this set to check your understanding.

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