Question

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

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

Answer 1

Answer: (C)

$si{n}^{-1}2x=co{s}^{-1}x$
$si{n}^{-1}2x=si{n}^{-1}\sqrt{1-x^2}$
$\Rightarrow 2x=\sqrt{1-x^2}$
$\Rightarrow 4x^2=1-x^2$
$\Rightarrow x=\pm \frac{1}{\sqrt{5}}$
$x=\frac{1}{\sqrt{5}}\left(\because x\ne -\frac{1}{\sqrt{5}}\right)$