prove that
(1-sina-cosa)^2=2(1-sina)(1-cosa)
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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)
LHS=RHS
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