Simplify to a basic equation, find $\alpha$ from $|value|$, let the sign choose quadrants (ASTC), then list all solutions in range.

Reflex: Basic angle from |value|; sign picks quadrants; range decides ±360° copies.

Divide both sides by $\cos x$. One basic equation, two quadrants, done. E.g. $3\sin x=2\cos x\Rightarrow \tan x=\frac23\Rightarrow x=33.7°,213.7°$. Reflex: See sin□ = cos□ → divide by cos, get tangent (safe: cos x=0 would force sin x=0 too).

Dividing by $\cos x$ silently kills the solutions $x = 90°, 270°$. Bring all terms to one side and factorize instead. Reflex: Common trig factor → factorize, never cancel. Each factor is its own equation.

Pick the $\cos 2x$ form matching the other function, move everything to one side. Reflex: Unify the angle → one side → factorize → solve each factor with the basic-angle routine.