Question:
If $x=\sin ^{-1}(\sin 10)$ and $y=\cos ^{-1}(\cos 10)$, then $y-x$ is equal to.
Correct Option: , 4
Solution:
$x=\sin ^{-1}(\sin 10)$
$\Rightarrow \quad x=3 \pi-10$ $\left\{\begin{array}{l}3 \pi-\frac{\pi}{2}<10<3 \pi+\frac{\pi}{2} \\ \Rightarrow 3 \pi-x=10\end{array}\right.$
and $y=\cos ^{-1}(\cos 10)$ $\left\{\begin{array}{l}3 \pi<10<4 \pi \\ \Rightarrow 4 \pi-x=10\end{array}\right.$
$\Rightarrow \quad y=4 \pi-10$
$\therefore \quad y-x=(4 \pi-10)-(3 \pi-10)=\pi$
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