Question

SinA-cosA=1/2 find sinA+cosA

Answer 1

sinA - cosA = 1/2

squaring both sides

(sinA - cosA)² = (1/2)²
⇒sin²A + cos²A - 2 sinAcosA = 1/4
⇒1 - 2 sinAcosA = 1/4
⇒2sinAcosA = 1- (1/4) = 3/4

now, (sinA +cosA)² = sin²A + cos²A + 2 sinAcosA
                              = 1 + 3/4 = 7/4
∴sinA + cosA = √(7/4) = (√7)/2