Question

If x cos (a + y) = cos y, then prove that dy/dx = cos²(a + y)/sin a. Hence, show that sin a d²y/dx² + sin2(a + y)dy/dx = 0.

Answer 1

Given, x cos (a + y) = cos y

On differentiating both sides w.r.t. y, we get

[by using quotient rule of derivative]

['.' sin A cos B - cos A sin B = sin (A - B)]

Again on differentiating both sides of Eq. (1) w.r.t. x, we get