If `(1)/(sqrt2) lt x lt 1`, then prove that `cos^(-1) x + cos^(-1) ((x + sqrt(1 - x^(2)))/(sqrt2)) = (pi)/(4)`

Explanation

To prove that

\[ \cos^{-1} x + \cos^{-1} \left( \frac{x + \sqrt{1 - x^2}}{\sqrt{2}} \right) = \frac{\pi}{4} \]

for \( \frac{1}{\sqrt{2}} < x < 1 \), we will follow the steps outlined below:

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