Question

If the equation ${\sin }^{-1}x={\text{cosec}}^{-1}x$ is satisfied for $\alpha$ and $\beta$, $(\alpha \ne \beta )$, then $\alpha +\beta$ is equal to

Answer 1

Answer: 0

${\sin }^{-1}x={\sin }^{-1}\left(\frac{1}{x}\right)$
$\Rightarrow x=\frac{1}{x}\Rightarrow x^2=1$
$x=\pm 1$
$\alpha =1\&\beta =-1$
hence $\alpha +\beta =0$