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

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(A) આપેલ પદાવલિ: $\frac{\sin ^{-1}(\cos x)+\cos ^{-1}(\sin x)}{	an ^{-1}(\cot x)+\cot ^{-1}(	an x)}$આપણે જાણીએ છીએ કે $\sin ^{-1} 	heta + \cos ^{-1

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(A) આપેલ પદાવલિ: $\frac{\sin ^{-1}(\cos x)+\cos ^{-1}(\sin x)}{	an ^{-1}(\cot x)+\cot ^{-1}(	an x)}$આપણે જાણીએ છીએ કે $\sin ^{-1} 	heta + \cos ^{-1} 	heta = \frac{\pi}{2}$ જ્યાં $	heta \in [-1, 1]$ અને $	an ^{-1} 	heta + \cot ^{-1} 	heta = \frac{\pi}{2}$ જ્યાં $	heta \in \mathbb{R}$.નિત્યસમ $\cos x = \sin(\frac{\pi}{2} - x)$ અને $\sin x = \cos(\frac{\pi}{2} - x)$ નો ઉપયોગ કરતા:અંશ: $\sin ^{-1}(\sin(\frac{\pi}{2} - x)) + \cos ^{-1}(\cos(\frac{\pi}{2} - x)) = (\frac{\pi}{2} - x) + (\frac{\pi}{2} - x) = \pi - 2x$.છેદ: $	an ^{-1}(	an(\frac{\pi}{2} - x)) + \cot ^{-1}(\cot(\frac{\pi}{2} - x)) = (\frac{\pi}{2} - x) + (\frac{\pi}{2} - x) = \pi - 2x$.આમ,પદાવલિ $\frac{\pi - 2x}{\pi - 2x} = 1$ થાય છે.

જો $x \neq n \pi, x \neq(2 n+1) \frac{\pi}{2}, n \in Z$ હોય,તો $\frac{\sin ^{-1}(\cos x)+\cos ^{-1}(\sin x)}{\tan ^{-1}(\cot x)+\cot ^{-1}(\tan x)}$ ની કિંમત શું થાય?

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