Question

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

• A. sin (a + y)
• B. sin² (a + y)
• C. $\frac{{\sin }^2(a+y)}{\sin a}$
• D. $\frac{\sin (a+y)}{\sin a}$

Answer 1

The Correct Option is C

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
\(=\frac{sin(a+y-y)}{sin^2(a+y)}\)
\(\Rightarrow \frac{dy}{dx}=\frac{sin^2(a+y)}{sina}\)