Question

Find `bb(dy/dx)` in the following:

sin² x + cos² y = 1

Answer 1

sin² x + cos² y = 1

Differentiating both sides with respect to x,

`d/dx sin^2 x + d/dx cos^2 y = d/dx (1)`

⇒ `2 sin x d/dx sin x + 2 cos y d/dx cos y = 0`

⇒ `2 sin x cos x + 2 cos y (- sin y) dy/dx = 0`

⇒ `2 sin x cos x - 2 cos y sin y dy/dx = 0`

⇒ `sin 2x - sin 2y dy/dx = 0`

∴ `dy/dx = (sin 2x) /(sin 2y)`