Question

Prove that (1-sinA+cosA)^2=2(1-sinA)(1+cosA)

Answer 1

By using identity,

(a-b+c)^2 = a^2+b^2+c^2-2ab-2bc+2ca

(1-sinA+cosA)^2 = 1+sin^2 A + cos^2 A - 2sinA - 2sinAcosA + 2cosA

= 2 - 2sinA -2sinAcosA + 2cosA

= 2(1+cosA) - 2sinA(1 + cosA)

= (2-2sinA)(1+cosA)

= 2(1-sinA)(1+cosA)