Question

If cos y = x cos(a + y) with cos a ≠ ± 1, then `dy/dx` is equal to ______ 

Options

• `sina/(cos^2(a + y))`

• `(cos^2(a + y))/sina`

• `cosa/(sin^2(a + y))`

• `(cos^2(a + y))/cosa`

Answer 1

If cos y = x cos(a + y) with cos a ≠ ± 1, then `dy/dx` is equal to `underline((cos^2(a + y))/sina)`.

Explanation:

cos y = x cos(a + y) 

⇒ x = `cosy/(cos(a + y))`

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

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

⇒ `1 = (dy/dx sin(a + y - y))/(cos^2(a + y))`

⇒ `dy/dx = (cos^2(a + y))/sina`