Question

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

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

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

(c) $\sin a \sin ^2(a+y)$

(d) $\frac{\sin ^2(a-y)}{\sin a}$

Answer 1

SOLUTION — Given, $x=\frac{\sin y}{\sin (a+y)}$

On differentiating w.r.t. $y$, we get

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

$\Rightarrow  \frac{d x}{d y}=\frac{\sin (a+y-y)}{\sin ^2(a+y)} \\$

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

So, The correct option of this question will be (B).