If y = log sqrt{tan x},then the value of frac | vedclass

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(A) Given $y = \log \sqrt{	an x} = \frac{1}{2} \log(	an x)$.Applying the chain rule,we differentiate with respect to $x$:$\frac{dy}{dx} = \frac{1}{2

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(A) Given $y = \log \sqrt{	an x} = \frac{1}{2} \log(	an x)$.Applying the chain rule,we differentiate with respect to $x$:$\frac{dy}{dx} = \frac{1}{2} 	imes \frac{1}{	an x} 	imes \sec^2 x$.Using the identities $	an x = \frac{\sin x}{\cos x}$ and $\sec^2 x = \frac{1}{\cos^2 x}$,we get:$\frac{dy}{dx} = \frac{1}{2} 	imes \frac{\cos x}{\sin x} 	imes \frac{1}{\cos^2 x} = \frac{1}{2 \sin x \cos x} = \frac{1}{\sin(2x)}$.Now,substitute $x = \frac{\pi}{4}$:$\left(\frac{dy}{dx}ight)_{x=\frac{\pi}{4}} = \frac{1}{\sin(2 	imes \frac{\pi}{4})} = \frac{1}{\sin(\frac{\pi}{2})} = \frac{1}{1} = 1$.

If $y = \log \sqrt{\tan x}$,then the value of $\frac{dy}{dx}$ at $x = \frac{\pi}{4}$ is

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