JEE PYQ: Trigonometric Equations And Inequations Question 9
Question 9 - 2020 (07 Jan Shift 2)
If $\theta_1$ and $\theta_2$ be respectively the smallest and the largest values of $\theta$ in $(0, 2\pi) - {\pi}$ which satisfy the equation, $2\cot^2 \theta - \frac{5}{\sin \theta} + 4 = 0$, then $\int_{\theta_1}^{\theta_2} \cos^2 3\theta , d\theta$ is equal to:
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(1) $\frac{\pi}{3}$
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(2) $\frac{2\pi}{3}$
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(3) $\frac{\pi}{3} + \frac{1}{6}$
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(4) $\frac{\pi}{9}$
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Answer:
Solution
$2\sin^2\theta - 5\sin\theta + 2 = 0 \Rightarrow \sin\theta = \frac{1}{2} \Rightarrow \theta = \frac{\pi}{6}, \frac{5\pi}{6}$
$\int_{\pi/6}^{5\pi/6} \cos^2 3\theta , d\theta = \frac{\pi}{3}$
BETA
