Question

If sin y = x sin (a + y), then dydxis

• A. sin (a + y)
• B. sin2 (a + y)
• C. sin2⁡(a+y)sin⁡a
• D. sin⁡(a+y)sin⁡a

Answer 1

Answer: (C)

sin2⁡(a+y)sin⁡a

Answer 2

Explanation:
$\frac{dy}{dx} = \frac{sin(a+y) cosy - siny cos(a+y)}{sin^2(a+y)}$
$x = \frac{siny}{sin(a+y)}$
On differentiating w.r.t. y, we get
$=\frac{sin(a+y-y)}{sin^2(a+y)}$
$\Rightarrow \frac{dy}{dx}=\frac{sin^2(a+y)}{sina}$