Elementary equation in cosine

Statement

Solve the following equation with sine/cosine, finding both solutions: $2+3\cos(\alpha)=3-2\cos(\alpha)$

Solution

Collect the terms in $\cos\alpha$: $3\cos\alpha+2\cos\alpha=3-2\Rightarrow 5\cos\alpha=1\Rightarrow \cos\alpha=\frac15=0.2.$ Since $\arccos(0.2)\approx 78.46°$, the two solutions are $\alpha\approx \pm 78.46°+360°k,\qquad k\in\mathbb{Z}.$

$\boxed{\cos\alpha=\tfrac15\ \Rightarrow\ \alpha\approx\pm 78.46°+360°k}$