Let $S = \left\{ {\theta \in \left[ { - \pi ,\pi } \right] - \left\{ { \pm \frac{\pi }{2}} \right\}:\sin \theta \tan \theta + \tan \theta = \sin 2\theta } \right\}.$ If $T = \sum\limits_{\theta \in S} {\cos 2\theta } ,$ then $T + n\left( S \right)$ is equal to:

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Analyzing +4 | -1

Let

S = \left\{ {\theta \in \left[ { - \pi ,\pi } \right] - \left\{ { \pm \frac{\pi }{2}} \right\}:\sin \theta \tan \theta + \tan \theta = \sin 2\theta } \right\}.

T = \sum\limits_{\theta \in S} {\cos 2\theta } ,

then

T + n\left( S \right)

is equal to:

View answer and explanation

Correct option: B

The correct answer is 9 because the sum of the cosines of the solutions plus the number of solutions to the trigonometric equation equals 9.

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