If int frac{f(x) , dx}{log sin x} = log log s | vedclass

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(D) Given the equation: $\int \frac{f(x) \, dx}{\log \sin x} = \log \log \sin x$. To find $f(x)$,we differentiate both sides with respect to $x$ using

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$\cot x$

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(D) Given the equation: $\int \frac{f(x) \, dx}{\log \sin x} = \log \log \sin x$. To find $f(x)$,we differentiate both sides with respect to $x$ using the Fundamental Theorem of Calculus and the Chain Rule. Let $y = \log \sin x$. Then $\frac{dy}{dx} = \frac{1}{\sin x} \cdot \cos x = \cot x$. By differentiating the right side: $\frac{d}{dx} (\log(\log \sin x)) = \frac{1}{\log \sin x} \cdot \frac{d}{dx}(\log \sin x) = \frac{1}{\log \sin x} \cdot \cot x$. Equating the derivatives: $\frac{f(x)}{\log \sin x} = \frac{\cot x}{\log \sin x}$. Therefore,$f(x) = \cot x$.

If $\int \frac{f(x) \, dx}{\log \sin x} = \log \log \sin x$,then $f(x) = $

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