Recall that cos(x-A) = cosx cos A + sin x sinA
Then B cos(x-A) = B cosA cosx + B sinA sinx
This equals 2 cos x + sin x, so B cosA = 2 and B sin A =1 (equating the terms)
Then you have 2 simul equations to solve for B and A. (to give B= sqr 5 and A = tan^-1(1/2)