JEE PYQ: Trigonometric Ratios And Identities Question 12
Question 12 - 2019 (10 Jan Shift 2)
The value of $\cos\frac{\pi}{2^2} \cdot \cos\frac{\pi}{2^3} \cdots \cos\frac{\pi}{2^{10}} \cdot \sin\frac{\pi}{2^{10}}$ is:
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(1) $\frac{1}{512}$
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(2) $\frac{1}{1024}$
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(3) $\frac{1}{256}$
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(4) $\frac{1}{2}$
Show Answer
Answer: (1) $\frac{1}{512}$
Solution
Repeatedly applying $\cos\theta \cdot \sin\theta = \frac{1}{2}\sin 2\theta$: $= \frac{1}{2^9}\sin\frac{\pi}{2} = \frac{1}{512}$.
BETA
