Question

If $y={\sin }^{-1}(\cos x),$ then $\frac{dy}{dx}$ is equal to:

• A. $\frac{1}{\sin x}$
• B. ${\cos }^{-1}x$
• C. $-1$
• D. $\frac{1}{2}$

Answer 1

Answer: (C)

$y={\sin }^{-1}(\cos x)$
$={\sin }^{-1}\left(\sin \left(\frac{\pi }{2}-x\right)\right)$
$\Rightarrow$ $y=\frac{\pi }{2}-x$
On differentiating both sides, w.r.t. $x,$ we get
$\frac{dy}{dx}=-1$