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Prove that: tan^(-1){(sqrt(1+x)-sqrt(1-...

Prove that: tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}=pi/4-1/2. cos^(-1)x , 0

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To prove that \[ \tan^{-1}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right) = \frac{\pi}{4} - \frac{1}{2} \cos^{-1}(x), \quad 0 < x < 1, \] we will follow these steps: ...
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