Prove the following (1) sin−1(2x1+x2)=2tan−1x, |x|≤1 (2) cos−1 – InterviewSolution

1.	Prove the following (1) sin−1(2x1+x2)=2tan−1x, \|x\|≤1 (2) cos−1(1−x21+x2)=2tan−1x, x≥0 (3) tan−1(2x1−x2)=2tan−1x, −1<x<1
Answer» Prove the following $(1) {sin}^{- 1} (\frac{2 x}{1 + x^{2}}) = 2 {tan}^{- 1} x, \| x \| \leq 1$ $(2) {cos}^{- 1} (\frac{1 - x^{2}}{1 + x^{2}}) = 2 {tan}^{- 1} x, x \geq 0$ $(3) {tan}^{- 1} (\frac{2 x}{1 - x^{2}}) = 2 {tan}^{- 1} x, - 1 < x < 1$

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