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