数学基础定义&定理整理
1. 三角函数 1.1 基础定义 $\tan \theta = \frac{\sin \theta}{\cos \theta}$ $\csc \theta = \frac{1}{\sin \theta}, \quad \sec \theta = \frac{1}{\cos \theta}, \quad \cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta}$ 1.2 基本恒等式 毕达哥拉斯恒等式: $\sin^2 \theta + \cos^2 \theta = 1$ 和差公式: \[ \begin{aligned} \sin(\alpha \pm \beta) &= \sin \alpha \cos \beta \pm \cos \alpha \sin \beta \\ \cos(\alpha \pm \beta) &= \cos \alpha \cos \beta \mp \sin \alpha \sin \beta \\ \tan(\alpha \pm \beta) &= \frac{\tan \alpha \pm \tan \beta}{1 \mp \tan \alpha \tan \beta} \end{aligned} \] ...