Question

If $x={\sin }^{-1}\left(\sin 10\right)$ and $y={\cos }^{-1}\left(\cos 10\right)$, then find $y-x$.

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

Answer 1

The correct option is A $\pi$

Given, $x=si{n}^{-1}\left(sin10\right)$

$x=3\pi -10$

Also,

$y=co{s}^{-1}\left(cos10\right)$

$y=4\pi -10$

Therefore,

$y-x=4\pi -10-3\pi +10=\pi$