Question

Prove the following identities :

cos⁴ A + sin⁴ A + 2 sin² A. cos² A = 1

Answer 1

Taking LHS = cos⁴ A + sin⁴ A + 2 sin² A cos² A

Using the identity,(a + b)² = (a² + b² + 2ab)

Here, a = cos² A and b = sin² A

= ( cos² A + sin² A) [∵ cos² θ + sin² θ = 1]

= 1