Differentiate `sin^(-1)((2x)/(1+x^2))` with respect to `cos^(-1)((1-x^2)/(1+x^2))` , if `0

Explanation

Let `P=\sin ^{-1} \frac{2 x}{1+x^{2}}=2 \tan ^{-1} x`


And `q=\cos ^{-1} \frac{1-x^{2}}{1+x^{2}}=2 \tan ^{-1} x`



`\therefore \frac{{dp}}{{dx}}=\frac{2}{1+{x}^{2}}=\text { and } \frac{{dq}}{{dx}}=\frac{2}{1+{x}^{2}}`



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