Solving trigonometric equations (factorization, homogeneous, change of variable)

Trigonometric equations: where to start

Goal — find all $x$ on a given set (often $\mathbb{R}$ or an interval) where the equality holds. You usually simplify the left-hand side (formulas from the previous lesson, identities), then use one of the techniques here: factoring, homogeneous equations, substitution. Domain: dividing by $\sin x$ , $\cos x$ , $\tan x$ , etc. is allowed only where the divisor is nonzero; excluded points are checked separately or reflected in the final answer. Period: for $\sin$ and $\cos$ add $+2\pi k$ , $k\in\mathbb{Z}$ to partial solutions; for $\tan$ and $\cot$ — $+\pi k$ (unless stated otherwise).

First try factoring — the most direct route when it is obvious

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