Prove the following identities :(sinθ + cosθ)2 + (sinθ – cosθ)2

1.	Prove the following identities :(sinθ + cosθ)2 + (sinθ – cosθ)2 = 2
Answer» Taking LHS = (sin θ + cos θ)² + (sin θ – cos θ)² Using the identity,(a + b)² = (a² + b² + 2ab) and (a – b)² = (a² + b² – 2ab) = sin² θ + cos² θ + 2sin θ cos θ + sin² θ + cos² θ – 2sin θ cos θ = 1 +1 [∵ cos² θ + sin² θ = 1] = 2 = RHS Hence Proved

Prove the following identities :(sinθ + cosθ)2 + (sinθ – cosθ)2 = 2

Answer»

Taking LHS = (sin θ + cos θ)² + (sin θ – cos θ)²

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

= sin² θ + cos² θ + 2sin θ cos θ + sin² θ + cos² θ – 2sin θ cos θ

= 1 +1 [∵ cos² θ + sin² θ = 1]

= 2

= RHS

Hence Proved