Question

The value of $si{n}^{-1}\left(cos\right(co{s}^{-1}\left(cosx\right)+si{n}^{-1}\left(sinx\right)\left)\right)$, where $xϵ(\frac{\pi }{2},\pi )$, is equal to

• A. $\frac{\pi }{2}$
• B. $-\pi$
• C. $\pi$
• D. $-\frac{\pi }{2}$

Answer 1

The correct option is D $-\frac{\pi }{2}$

$si{n}^{-1}\left[cosco{s}^{-1}\right(cos\left(x\right)+si{n}^{-1}\left(sin\right(x\left)\right)]$
$=si{n}^{-1}\left[cos\right(x+\pi -x\left)\right]$
$=si{n}^{-1}\left[cos\right(\pi \left)\right]]$
$=si{n}^{-1}(-1)$
$=\frac{-\pi }{2}$