If x neq n pi, x neq(2 n+1) frac{pi}{2}, n in | vedclass

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(A) Given expression: $\frac{\sin ^{-1}(\cos x)+\cos ^{-1}(\sin x)}{	an ^{-1}(\cot x)+\cot ^{-1}(	an x)}$We know that $\sin ^{-1} 	heta + \cos ^{-1

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(A) Given expression: $\frac{\sin ^{-1}(\cos x)+\cos ^{-1}(\sin x)}{	an ^{-1}(\cot x)+\cot ^{-1}(	an x)}$We know that $\sin ^{-1} 	heta + \cos ^{-1} 	heta = \frac{\pi}{2}$ for $	heta \in [-1, 1]$ and $	an ^{-1} 	heta + \cot ^{-1} 	heta = \frac{\pi}{2}$ for $	heta \in \mathbb{R}$.Using the identities $\cos x = \sin(\frac{\pi}{2} - x)$ and $\sin x = \cos(\frac{\pi}{2} - x)$:Numerator: $\sin ^{-1}(\sin(\frac{\pi}{2} - x)) + \cos ^{-1}(\cos(\frac{\pi}{2} - x)) = (\frac{\pi}{2} - x) + (\frac{\pi}{2} - x) = \pi - 2x$.Denominator: $	an ^{-1}(	an(\frac{\pi}{2} - x)) + \cot ^{-1}(\cot(\frac{\pi}{2} - x)) = (\frac{\pi}{2} - x) + (\frac{\pi}{2} - x) = \pi - 2x$.Thus,the expression becomes $\frac{\pi - 2x}{\pi - 2x} = 1$.

If $x \neq n \pi, x \neq(2 n+1) \frac{\pi}{2}, n \in Z$,then $\frac{\sin ^{-1}(\cos x)+\cos ^{-1}(\sin x)}{\tan ^{-1}(\cot x)+\cot ^{-1}(\tan x)}$ is

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