Prove that (1-sinA+cosA)2=2(1-sinA)(1+cosA)
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Step-by-step explanation:
(1-sinA+cosA)²={(1-sinA)+cosA}²
=(1-sinA)²+2(1-sinA)cosA+cos²A
=1-2sinA+sin²A+2(1-sinA)cosA+cos²A
=2-2sinA+2(1-sinA)cosA
=2(1-sinA)+2(1-sinA)cosA
=2(1-sinA)(1+cosA)
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