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  4. If |x| le 1, then 2 tan-1x + sin-1 ((2x/1+x2)) is equal to

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Q. If $\left|x\right| \le 1$, then $2 \,tan^{-1}x + sin^{-1} \left(\frac{2x}{1+x^{2}}\right)$ is equal to

Inverse Trigonometric Functions

Solution:

$ 2 \,tan^{-1}x + sin^{-1} \frac{2x}{1+x^{2}}$
$=2tan^{-1}x+2tan^{-1}x=4tan^{-1}x$