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