Question

if cosA + sinA = 1, prove that cosA - sinA = +or-1​

Answer 1

cosA + sinA = 1

squaring both side we get

(cosA + sinA)^2 = 1

cos^2A + sin^2A + 2sinAcosA = 1

1 + 2sinAcosA = 1

2sinAcosA = 0

now

(cosA - sinA)^2 = cos^2A + sin^2A - 2sinAcosA

(cosA - sinA)^2 = 1 - 2sinAcosA

but 2sinAcosA = 0

(cosA - sinA)^2 = 1

square root both side we get

cosA - sinA = +1 or -1