What is the smallest positive $ x $ satisfying $ \log_{\sin x} \cos x + \log_{\cos x} \sin x = 2 $ ?

Question

SquadPrep · Accepted Answer

{4}. Let y = \log_{\sin x} \cos x. The equation becomes y + 1/y = 2, which gives y = 1. So \log_{\sin x} \cos x = 1, leading to \sin x = \cos x. The smallest positive x satisfying this is \pi/4.

Answer

{2}

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{3}

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{6}

What is the smallest positive \( x \) satisfying \( \log_{\sin x} \cos x + \log_{\cos x} \sin x = 2 \) ?

Explanation

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