$$
\begin{align*}
\textbf{I: 基本恒等式}\notag \\
\sin^2 x + \cos^2 x &= 1 \\
\tan x &= \frac{\sin x}{\cos x} \\
1 + \tan^2 x &= \sec^2 x \\
1 + \cot^2 x &= \csc^2 x \\
\hline
\textbf{II: 诱导公式} \notag \\
(奇变偶不变，符号看象限) \notag \\
\sin(x+2k\pi) &= \sin x \\ \cos(x+2k\pi) &= \cos x \\ \tan(x+k\pi) &= \tan x
\\ \hdashline
\sin(-x) &= -\sin x \\ \cos(-x) &= \cos x \\ \tan(-x) &= -\tan x
\\ \hdashline
\sin(\pi - x) &= \sin x \\ \cos(\pi - x) &= -\cos x
\\ \hdashline
\sin(\pi + x) &= -\sin x \\ \cos(\pi + x) &= -\cos x
\\ \hdashline
\sin(\frac{\pi}{2}-x)&=\cos x \\
\cos(\frac{\pi}{2}-x)&=\sin x
\\ \hdashline
\sin(\frac{\pi}{2}+x)&=\cos x \\
\cos(\frac{\pi}{2}+x)&=-\sin x \\
\hline
\textbf{III: 和差公式} \\
\sin(a\pm b)&=\sin a\cos b\pm\cos a\sin b \\
\cos(a\pm b)&=\cos a\cos b\mp\sin a\sin b \\
\tan(a\pm b)&=\frac{\tan a\pm\tan b}{1\mp\tan a\tan b} \\
\hline
\textbf{IV: 二倍角公式} \\
\sin 2x &= 2\sin x\cos x \\
\cos 2x &= \cos^2 x - \sin^2 x \\
&= 1 - 2\sin^2 x \\
&= 2\cos^2 x - 1 \\
\tan 2x &= \frac{2\tan x}{1-\tan^2 x} \\
\hline
\textbf{V: 半角公式} \\
\sin^2\frac{x}{2} &= \frac{1-\cos x}{2} \\
\cos^2\frac{x}{2} &= \frac{1+\cos x}{2} \\
\tan\frac{x}{2} &= \frac{\sin x}{1+\cos x} \\
\tan\frac{x}{2} &= \frac{1-\cos x}{\sin x} \\
\tan\frac{x}{2} &= \frac{\sin x}{1+\cos x} \\
\end{align*}
$$