Q. If $y = \sqrt{\sin{x + \sqrt{\sin{x + \sqrt{\sin{x + \ldots\infty}}}}}}$, then $(2y - 1)\frac{dy}{dx}\$is equal to
A) $\sin x$
B) $- \cos x$
C) $\cos x$
D) $- \sin x$
Explanation
(c)
Given, $y = \sqrt{\sin{x + y}}$ $\Rightarrow {\ \ \ \ \ y}^{2} = {sin\ }{x + y\ }$
$\Rightarrow 2y\ \frac{dy}{dx} = \cos{x + \frac{dy}{dx}}$
$\Rightarrow (2y - 1)\frac{dy}{dx} = \cos x$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.