JEE PYQ: Trigonometric Equations And Inequations Question 17
Question 17 - 2019 (10 Jan Shift 1)
The sum of all values of $\theta \in \left(0, \frac{\pi}{2}\right)$ satisfying $\sin^2 2\theta + \cos^4 2\theta = \frac{3}{4}$ is:
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(1) $\pi$
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(2) $\frac{5\pi}{4}$
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(3) $\frac{\pi}{2}$
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(4) $\frac{3\pi}{8}$
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Answer:
Solution
By AM–GM, $\cos^2 2\theta = \frac{1}{2} \Rightarrow \theta = \frac{\pi}{8}, \frac{3\pi}{8}$
Sum $= \frac{\pi}{8} + \frac{3\pi}{8} = \frac{\pi}{2}$
BETA
