Hello Paymemoney
Hi

Can someone tell me how to do this question:

1) Convert 4sin2x+5cos2x into a single cosine wave form Acos(2x+C)

P.S

Just to expand a little on *mathaddict*'s reply, use the identity\(\displaystyle \cos(P+Q) = \cos P \cos Q - \sin P \sin Q\)

as follows:\(\displaystyle A\cos(2x+C) = 4\sin 2x +5\cos 2x\)

\(\displaystyle \Rightarrow A\cos2x\cos C -A\sin2x\sin C = 4\sin2x+5\cos2x\)

\(\displaystyle \Rightarrow \left\{\begin{array}{l l}A\cos C = 5 & \quad\text{(1)}\\ A\sin C = -4&\quad\text{(2)}\end{array}\right.\)

Square (1) and (2) and add:

\(\displaystyle A^2 = 5^2+(-4)^2\)

\(\displaystyle \Rightarrow A = \sqrt{41}\)

Divide (2) by (1):

\(\displaystyle \tan C = -\tfrac45\)

Grandad