JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Let

S = \left\{ {0 \in \left( {0,\frac{\pi }{2}} \right):\sum\limits_{m = 1}^9 {\sec \left( {\theta + \left( {m - 1} \right)\frac{\pi }{6}} \right)\sec \left( {\theta + \frac{{m\pi}}{6}} \right) = - \frac{8}{{\sqrt 3 }}} } \right\}.

Then

View answer and explanation

Correct option: C

\sum\limits_{\theta \in S} {\theta = \frac{\pi }{2}}

Option C (

\sum\limits_{\theta \in S} {\theta = \frac{\pi }{2}}

) is correct because solving the trigonometric equation leads to two solutions for

\theta

, and their sum is

\frac{\pi}{2}

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