Question

cos⁴ θ – sin⁴ θ is equal to ______.

Options

• `1 + 2 sin^2 (θ/2)`

• 2 cos² θ – 1

• `1 - 2 sin^2 (θ/2)`

• 1 + 2 cos² θ

Answer 1

cos⁴ θ – sin⁴ θ is equal to 2 cos² θ – 1.

Explanation:

cos⁴ θ – sin⁴ θ = (cos² θ – sin² θ)(cos² θ + sin² θ)

= cos 2 θ

= 2 cos² θ – 1