If x sin(a + y) + sin a cos(a + y) = 0, then show dy/dx = sin^2(a + y)/sin a

Question

If x sin(a + y) + sin a cos(a + y) = 0, then show dy/dx \(=\frac{sin^2(a + y)}{sin\,a}\)

= sin²(a + y)/sin a

Answer 1

x sin(a + y) + sin a . cos (a + y) = 0 ….. (1)

Differentiating w.r.t. x, we get

Alternative Method :

Differentiating both sides w.r.t. y, we get