Question

If value of x which satisfy equation ${\sin }^{-1}x>-1$ is $xϵ(a,b]$.
Find the value of $a+b$.

• A. $-\sin 1$
• B. $-\sin 1-1$
• C. $\sin 1+1$
• D. $-\sin 1+1$

Answer 1

The correct option is D $-\sin 1+1$

Given, ${\sin }^{-1}x>-1$
Also we know that $-\frac{\pi }{2}\le {\sin }^{-1}x\le \frac{\pi }{2}$
$\Rightarrow -1<{\sin }^{-1}x\le \frac{\pi }{2}$
or $\sin (-1)<x\le \sin \left(\frac{\pi }{2}\right)$
$\Rightarrow$ $xϵ(-\sin 1,1]$