Question

If $x={\sin }^{-1}\left(\sin 10\right)$ and $y={\cos }^{-1}\left(\cos 10\right)$, then $y-x$ is equal to :

• A. $0$
• B. $\pi$
• C. $10$
• D. $7\pi$

Answer 1

The correct option is B $\pi$

$x={\sin }^{-1}\left(\sin 10\right)$
$\Rightarrow x={\sin }^{-1}\left(\sin \right(3\pi -10\left)\right)$
$\Rightarrow x=3\pi -10$

Now, $y={\cos }^{-1}\left(\cos \right(10\left)\right)$
$\Rightarrow y={\cos }^{-1}\left(\cos \right(4\pi -10\left)\right)$
$\Rightarrow y=4\pi -10$
$\therefore y-x=4\pi -10-3\pi +10$
$\Rightarrow y-x=\pi$