Question

Prove that:
(1-sin A +cos a) = 2(1-sin A) (1+COSA)​

Answer 1

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,sin2+cos2A=1]

= 2 − 2sinA + 2(1-sinA)cosA

= 2(1 − sinA) + 2(1-sinA)cosA

= 2(1 − sinA)(1 + cosA)

= RHS

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