Question

If sin y = x sin(a + y), then `dy/dx` = ______ 

Options

• `(sin^2(a + y))/(sin(a + y))`

• `(sin^2(a + y))/(cos(a + 2y))`

• `(sin^2(a + y))/sina`

• `(sin^2(a + y))/cosa`

Answer 1

If sin y = x sin(a + y), then `dy/dx` = `underline((sin^2(a + y))/sina)`

Explanation:

sin y = x sin(a + y)

⇒ x = `siny/(sin(a + y))`

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

I = `(sin(a + y).cosy dy/dx - siny.cos(a + y)dy/dx)/(sin^2(a + y))`

⇒ I = `(dy/dx.sin(a + y - y))/(sin^2(a + y))`

⇒ `dy/dx = (sin^2(a + y))/(sina)`