Question

Evaluate the following:

(sin θ + cos θ)² + (sin θ – cos θ)²

Answer 1

Given (sin θ + cos θ)² + (sin θ – cos θ)² 

= (sin² θ + cos² θ + 2 sin θ cos θ) + (sin² θ + cos² θ – 2 sin θ cos θ) [∵ (a + b)² = a² + b² + 2ab (a – b)² = a² + b² – 2ab]

= 1 + 2 sin θ cos θ + 1 – 2 sin θ cos θ [∵ sin²  θ + cos² θ = 1] 

= 1 + 1 

= 2