If a cosA - b sinA = c . Prove that a sinA + b cosA = _+√a^2 + b^2 - c^2

Answer 1

let a = sinB and let b = cosB
then a cosA - b sinA
= sinBcosA - cosBsinA
= sin(B-A)
= c

and a sinA + b cosA
= sinBsinA + sinAcosA
= cos(A - B)
= cos(B-A) , since cos(-x) = cos(x)

let's look at the right side:
I will assume that should be
± √(a^2 + b^2 - c^2)
= √(sin^2 B + cos^2 B - sin^2 (B-A) )
= √(1 - cos^2 (B-A))
= √ cos^2 (B-A)
= ± cos(B-A)
= a sinA + b cosA
as required

Whewww!!! tricky, does somebody see a better way?