Question

(1-sinA+cosA)²=2(1+cosA)(1-sinA)

Answer 1

LHS

[(1-SinA)+cosA)^2

using formula (a+b)^2 =a^2+b^2+2ab

(1-sinA)^2 + cos^2A + 2cosA(1-sinA)

now using formula (a-b)^2= a^2+ b^2-2ab

1+sin^2A-2sinA+cos^2A+2 cosA(1-sinA)

we know that sin^2A+cos^2A=1

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

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

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

2(1-sinA)[1+cosA]

hence prooved

Answer 2

Step-by-step explanation:

(1-sinA+cosA)²=2(1+cosA)(1-sinA)

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