Science, asked by mnakum940, 11 months ago

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

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Answered by Anonymous

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Refer to the attachment!!

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Answered by ItzUnic0rns

109

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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)

$\therefore$ LHS=RHS

$\mathbb\red{HENCE\:\:PROVED}$

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