Formule trigonometrice pentru suma și diferența a două unghiuri

$$\begin{gathered} \cos (a+b)=\cos a\cos b-\sin a\sin b \\ \cos (a-b)=\cos a\cos b+\sin a\sin b \\ \sin (a+b)=\sin a\cos b+\cos a\sin b \\ \sin (a-b)=\sin a\cos b-\cos a\sin b, \forall a, b\in \mathrm{ℝ}. \\ tg(a+b)=\frac{tga+tgb}{1-tgatgb}, \forall a, b, a+b\in \mathrm{ℝ}-\left\{\left(2k+1\right)\frac{\pi }{2}\overline{)k\in \mathrm{\mathbb{Z}}}\right\} \\ tg(a-b)=\frac{tga-tgb}{1+tgatgb}, \forall a, b, a-b\in \mathrm{ℝ}-\left\{\left(2k+1\right)\frac{\pi }{2}\overline{)k\in \mathrm{\mathbb{Z}}}\right\} \end{gathered}$$