If `siny=xsin(a+y)` , then `(dy)/(dx)` is (a)`(sina)/(sina sin^2(a+y))` (b) `(sin^2(a+y))/(sina)` (c) `sina sin^2(a+y)` (d) `(sin^2(a-y))/(sina)`

Explanation

To find \(\frac{dy}{dx}\) given the equation \(\sin y = x \sin(a + y)\), we will follow these steps:

### Step 1: Differentiate both sides with respect to \(x\)
We start with the equation:
\[ \sin y = x \sin(a + y) \]
Differentiating both sides with respect to \(x\) using implicit differentiation:
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