If $y = sin\lbrack\cos^{- 1}{\{\sin{(\cos^{- 1}{x)\}\rbrack,\ then\frac{dy}{dx}\ at\ x = \frac{1}{2}\ }}}$is equal to

Question

Dr. Abubacker · Accepted Answer

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

Q. If $y = sin\lbrack\cos^{- 1}{\{\sin{(\cos^{- 1}{x)\}\rbrack,\ then\frac{dy}{dx}\ at\ x = \frac{1}{2}\ }}}$is equal to

Explanation

Reviewed by Dr. Abubacker

Want more practice?