Question

The solution set of the equation ${\sin }^{-1}x=2{\tan }^{-1}x$ is

• A. $\{1,2\}$
• B. $\{-1,2\}$
• C. $\{-1,1,0\}$
• D. $\left\{1,\frac{1}{2},0\right\}$

Answer 1

Answer: (C)

To find solution set of ${\sin }^{-1}x=2{\tan }^{-1}x={\sin }^{-1}\left(\frac{2x}{1+x^2}\right)$
$\Rightarrow x=\frac{2x}{1+x^2}$
$\Rightarrow x+x^3=2x$
$\Rightarrow x^3-x=0$
$\Rightarrow x\left(x^2-1\right)=0$
$\Rightarrow x=-1,1,0$