Maxima and minima

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Question

$If f (x) = {(\sin^{- 1} x)}^{2} + {(\cos^{- 1} x)}^{2} is stationary at x = a . Then a^{2} =$

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Solution

$\begin{array}{l} f^{1} (x) = 0 \\ \Rightarrow \sin^{- 1} x \Rightarrow \cos^{- 1} x \Rightarrow x = \frac{1}{\sqrt{2}} = a \\ \Rightarrow a^{2} = \frac{1}{2} = 0.5 \end{array}$

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