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

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π4

π6

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π3

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detailed solution

Correct option is A

We have logcosxsinx+logsinxcosx=2=1+11⇒logcosxsinx=1⇒sinx=cosx⇒tanx=1⇒x=π4

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The smallest positive x satisfying the equation logcosxsinx+logsinxcosx=2 is

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