Question

(1-sinA+ cosA)2=2(1-sinA) (1+cosA)​

Answer 1

Answer:

Consider the LHS:

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

= (1-sinA)2 + cos2A + 2(1-sinA)cosA

= 1 + sin2A − 2sinA + cos2A + 2(1-sinA)cosA

= 1 + (sin2A + cos2A) − 2sinA + 2(1-sinA)cosA

= 1 + 1 − 2sinA + 2(1-sinA)cosA [Since, sin2A + cos2A =1]

= 2 − 2sinA + 2(1-sinA)cosA

= 2(1 − sinA) + 2(1-sinA)cosA

= 2(1 − sinA)(1 + cosA)

= RHS

Hope it helps.