Question

The sum of all the solution(s) of the equation $sin^{- 1}2x=cos^{- 1}x$ is-

• A. $0$
• B. $\frac{2}{\sqrt{5}}$
• C. $\frac{1}{\sqrt{5}}$
• D. $\frac{- 1}{\sqrt{5}}$

Answer 1

Answer: (C)

$sin^{- 1}2x=cos^{- 1}x$
$sin^{- 1}2x=sin^{- 1}\sqrt{1 - x^{2}}$
$\Rightarrow 2x=\sqrt{1 - x^{2}}$
$\Rightarrow 4x^{2}=1-x^{2}$
$\Rightarrow x=\pm\frac{1}{\sqrt{5}}$
$x=\frac{1}{\sqrt{5}}\left(\because x \neq - \frac{1}{\sqrt{5}}\right)$