Discussion Forum



1)

If sin y = x sin(a+y), then $\frac{dy}{dx}$ is equal to


A) $\frac{\sin\sqrt{a}}{\sin\left(a+y\right)}$

B) $\frac{\sin^{2} (a+y)}{\sin a}$

C) $\sin(a+y)$

D) None of these

Answer:

Option B

Explanation:

Given, sin y = x sin (a + y)

$x = \frac{\sin y}{\sin(a+y)}$

$\frac{dx}{dy} = \frac{d}{dy}\left[\frac{\sin y}{\sin(a+y)}\right]$

 = $\frac{\sin(a+y)\cos y - \sin y\cos(a+y)}{\sin^{2}(a+y)}$

= $\frac{\sin a}{\sin^{2}(a+y)}$

$\frac{dy}{dx}= \frac{\sin^{2}(a+y)}{\sin a}$