Mathematics

Mathematics

Problem

Prove that tan⁡−1(1+x−1−x1+x+1−x)=π4−12cos⁡−1x\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, −12≤x≤1-\frac{1}{\sqrt{2}} \le x \le 1

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