Question

Cos⁴θ - Sin⁴θ = ?
Options:-
a) 1 + 2Sin²θ Cos²θ
b) 1 - 2Sin²θ Cos²θ
c) Cosθ - Sinθ
d) 1 - 2Sin²θ​

Answer 1

Cos⁴θ - Sin⁴θ

= (Cos²θ)² - (Sin²θ)²

By using a² - b² = (a + b)(a - b), we get

= (Cos²θ + Sin²θ) × (Cos²θ - Sin²θ)

We know that Cos²θ + Sin²θ = 1, and Cos²x - Sin²x = 2 Cosθ, we get

= 1 × 2(Cosθ)

= 2 Cosθ