Question

Prove the following identities:

sin⁴θ – cos⁴θ = 1 – 2cos²θ

Answer 1

LHS = (sin²θ + cos²θ) (sin²θ – cos²θ) 

= (sin²θ – cos²θ) 

= (1 – cos²θ – cos²θ) 

= (1 – 2cos²θ) = RHS