If `y={(log)_(cosx)sinx}{(log)_(sinx)cosx}^(-1)+sin^(-1)((2x)/(1+x^2)),`fin d`(dy)/(dx)a tx=pi/4`

Explanation

Let `y=(\log _{\sin x} \cos x)(\log _{\cos x} \sin x)^{-1}+\sin ^{-1}(2 x /(1+x^{2}))`



`arrow \quad y=\frac{\log (\cos x)}{\log (\sin x)} \times \frac{\log (\cos x)}{\log (\sin x)}+2 \tan ^{-1} x`




`arrow y=\frac{\{\log (\cos x)\}^{2}}{\{\log (\sin x)\}^{2}}+2 \tan ^{-1} x`




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