Question

If ${\left(sin\right)}^{-1}\left(sinx\right)=\pi -x,$ then $x$ belongs to $\left[\frac{a\pi }{b},\frac{c\pi }{d}\right]$ then the value of $a+b+c+d$ is equal to

Answer 1

Answer: 8

Given,
${\sin }^{-1}(\sin x)=\pi -x$
Now drawing the graph of ${\left(sin\right)}^{-1}\left(sinx\right)$ , we have

From the graph it is clear that
$x\in \left[\frac{\pi }{2},\frac{3\pi }{2}\right]$