Question

If sin theta - cos theta = 1/2 what is the value of sin theta + cos theta

Answer 1

sinθ - cosθ = 1/2
squaring both sides
(sinθ - cosθ)² = (1/2)²
⇒sin²θ + cos²θ - 2 sinθcosθ = 1/4
⇒1 - 2 sinθcosθ = 1/4
⇒2sinθcosθ = 1- (1/4) = 3/4

now, (sinθ +cosθ)² = sin²θ + cos²θ + 2 sinθcosθ
                              = 1 + 3/4 = 7/4
∴sinθ + cosθ = √(7/4) = (√7)/2