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 $