Question

If value of x which satisfy ${\sin }^{-1}x\le {\cos }^{-1}x$ is $xϵ[a,\frac{b}{\sqrt{c}}]$.
Find the value of $a+b+c$.

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is C 2

Given, ${\cos }^{-1}x\ge {\sin }^{-1}x$
Also we know that, ${\sin }^{-1}x+{\cos }^{-1}x=\frac{\pi }{2}$
Using above, $\frac{\pi }{2}\ge 2{\sin }^{-1}x$ or ${\sin }^{-1}x\le \frac{\pi }{2}$
or $-1\le x\le \sin \left(\frac{\pi }{4}\right)$
$\Rightarrow$ $xϵ[-1,\frac{1}{\sqrt{2}}]$