Question

The value of `(cos^3θ - cos 3θ)/cosθ + (sin^3θ + sin 3θ)/sinθ` is ______.

Options

• 4

• 5

• 3

• 2

Answer 1

The value of `(cos^3θ - cos 3θ)/cosθ + (sin^3θ + sin 3θ)/sinθ` is 3.

Explanation:

We have, `(cos^3θ - cos 3θ)/cosθ + (sin^3θ + sin 3θ)/sinθ`

= `(cos^3 θ - [4 cos^3 θ - 3 cos θ])/cosθ + (sin^3 θ + [3 sin θ - 4 sin^3 θ])/sinθ`

= `(-3 cos^3 θ + 3 cos θ)/cosθ + (3 sin θ - 3 sin^3 θ)/sinθ`

= `(3cos(1 - cos^2θ))/cosθ + (3 sin θ (1 - sin^2 θ))/sinθ`

= 3 sin² θ + 3 cos² θ

= 3 (sin² θ + cos² θ)

= 3(1)

= 3