Prove: ^ -1 ( 1+ x + 1- x 1+ x - 1- x ) = 4 + x 2 , 0 x 2 .
Mathematics · Class 12 · CBSE — Inverse Trigonometric Functions
Prove: \(\tan^{-1}\left(\frac{\sqrt{1+\cos x} + \sqrt{1-\cos x}}{\sqrt{1+\cos x} - \sqrt{1-\cos x}}\right) = \frac{\pi}{4} + \frac{x}{2}\), \(0 \lt x \lt \frac{\pi}{2}\).
Answer
Proved.
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