Question

If $\left(sin\right)^{- 1}\left(sin x\right)=\pi -x,$ 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

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

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