Question

If \[y = \sin^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) + \cos^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right),\text{ find } \frac{dy}{dx}\] ?

Answer 1

\[\text{ We have, y } = \sin^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) + \cos^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right)\]

\[ \Rightarrow y = \frac{\pi}{2} .............\left[ \because \sin^{- 1} x + \cos^{- 1} x = \frac{\pi}{2} \right]\]

\[\Rightarrow \frac{dy}{dx} = 0\]