Question

prove that: (1-sinA+cosA)²=2(1+cosA)(1-sinA)

Answer 1

Answer:

Step-by-step explanation:

Answer 2

(1-sinA+cosA)² = 2(1+cosA)(1-sinA)

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

(1-sinA)²+(cosA)²+2(1-sinA)(cosA)

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

1+sin²A+cos²A+2(1-sinA)(cosA)

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]