Question

Prove that Acosx + Bsinx = Rcos(x+c) where c = tan^-1(B/A) and R = sqrt(A^2+B^2)

Answer 1

Acosx + Bsinx = √(A^2+B^2) (A/√(A^2+B^2) cosx + B/√(A^2+B^2) sinx)

= √(A^2+B^2) (sinc cosx + cosc sinx)
= √(A^2+B^2) sin(c+x)