\sin(x+y)=\sin x\cos y + \cos x \sin y\\
\sin(x-y)=\sin x\cos y - \cos x \sin y\\
\cos(x+y)=\cos x\cos y - \sin x \sin y\\
\cos(x-y)=\cos x \cos y + \sin x \sin y
Dodatkowo:
Dla α,β,α+β,α−β∈R∖{x:x=2π+kπ,k∈Z}\displaystyle \alpha,\beta,\alpha+\beta,\alpha-\beta\in\mathbb{R}\setminus\left\{x:x= \frac{\pi}{2}+k\pi,k\in\mathbb{Z} \right\}:
tg(x+y)=1−tgxtgytgx+tgytg(x−y)=1+tgxtgytgx−tgy
\tg(x+y)=\frac{\tg x + \tg y}{1-\tg x\tg y}\\
\tg(x-y)=\frac{\tg x - \tg y}{1+\tg x \tg y}\\
Dla α,β,α+β,α−β∈R∖{x:x=2kπ,k∈Z}\displaystyle \alpha,\beta,\alpha+\beta,\alpha-\beta\in\mathbb{R}\setminus\left\{x:x= \frac{k\pi}{2},k\in\mathbb{Z} \right\}:
