Home 数学基础

万能代换公式

u=tan⁡x2sin⁡x=2u1+u2cos⁡x=1−u21+u2u = \tan \frac{x}{2} \\ \sin x = \frac{2u}{1 + u^2} \\ \cos x = \frac{1 - u^2}{1 + u^2}

积化和差公式

sin⁡xcos⁡y=12[sin⁡(x+y)+sin⁡(x−y)]cos⁡xsin⁡y=12[sin⁡(x+y)−sin⁡(x−y)]cos⁡xcos⁡y=12[cos⁡(x+y)+cos⁡(x−y)]sin⁡xsin⁡y=12[cos⁡(x−y)−cos⁡(x+y)]\sin x \cos y = \frac{1}{2} \left[ \sin (x+y) + \sin (x-y) \right] \\ \cos x \sin y = \frac{1}{2} \left[ \sin (x+y) - \sin (x-y) \right] \\ \cos x \cos y = \frac{1}{2} \left[ \cos (x+y) + \cos (x-y) \right] \\ \sin x \sin y = \frac{1}{2} \left[ \cos (x-y) - \cos (x+y) \right]