Inverse Trigonometric Functions

Prove that ????????????−????(√????+???? −√????−????)/(√????+???? + √????−????) =????/????-????/????????????????−???? ???? , −????√????≤ ???? ≤ ????[Hint: Put x = cos 2 θ]

Putting $x=\cos 2 \theta \quad$ so that, $\theta=\frac{1}{2} \cos ^{-1} x$ LHS $=\tan ^{-1}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right)$ $=\tan ^{-1}\left(\frac{\sqrt{1+\cos 2...

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