Auxiliary Angle/Examples/3 cos x minus 2 sin x equals 1

Example of Auxiliary Angle
Consider the equation:
 * $(1): \quad 3 \cos x - 2 \sin x = 1$

The solutions to $(1)$ between $0 \degrees$ and $360 \degrees$ are:

Proof
From Multiple of Sine plus Multiple of Cosine: Cosine Form:

Hence the auxiliary angle form of $(1)$ is given by: