A) \[\frac{\cot x\log \cos x+\tan x\log \sin x}{{{(\log \cos x)}^{2}}}\]
B) \[\frac{\tan x\log \cos x+\cot x\log \sin x}{{{(\log \cos x)}^{2}}}\]
C) \[\frac{\cot x\log \cos x+\tan x\log \sin x}{{{(\log \sin x)}^{2}}}\]
D) None of these
Correct Answer: A
Solution :
We have \[y={{\log }_{\cos x}}\sin x=\frac{\log \sin x}{\log \cos x}\] \[\therefore \frac{dy}{dx}=\frac{\cot x.\log \cos x+(\log \sin x)\tan x}{{{(\log \cos x)}^{2}}}\] .You need to login to perform this action.
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