– eki múyeshtiń qosındısı hám ayırmasınıń trigonometriyalıq funkciyaların usı múyeshlerdiń trigonometriyalıq funkciyaları arqalı ańlatıwǵa múmkinshilik beretuǵın formulalar: 1) $\cos(\alpha-\beta)=\cos\alpha \cos\beta+\sin\alpha \sin\beta$. 2) $\cos(\alpha+\beta)=\cos\alpha \cos\beta-\sin\alpha \sin\beta$. 3) $\sin(\alpha+\beta)=\sin\alpha \cos\beta+\cos\alpha \sin\beta$. 4) $\sin(\alpha-\beta)=\sin\alpha \cos\beta-\cos\alpha \sin\beta$. 5) $\text{tg}(\alpha+\beta)=\displaystyle\frac{\text{tg}\alpha+\text{tg}\beta}{1-\text{tg}\alpha \text{tg}\beta}$, $\alpha\neq(2k+1)\dfrac{\pi}{2}$, $k\in Z$, $\beta=(2m+1)\dfrac{\pi}{2}$, $m\in Z$, $\alpha+\beta\neq(2n+1)\dfrac{\pi}{2}$, $n\in Z$. 6) $\text{tg}(\alpha-\beta)=\displaystyle\frac{\text{tg}\alpha-\text{tg}\beta}{1+\text{tg}\alpha\text{tg}\beta}$, $\alpha\neq(2k+1)\dfrac{\pi}{2}$, $k\in Z$, $\beta=(2m+1)\dfrac{\pi}{2}$, $m\in Z$, $\alpha-\beta\neq(2n+1)\dfrac{\pi}{2}$, $n\in Z$ 7) $\text{ctg}(\alpha+\beta)=\dfrac{\text{ctg}\alpha\cdot\text{ctg}\beta-1}{\text{ctg}\alpha+\text{ctg}\beta}$, $\alpha\neq nk$, $k\in Z$, $\beta\neq\pi m$, $m\in Z$, $\alpha+\beta\neq\pi n$, $n\in Z$. 8) $\text{ctg}(\alpha-\beta)=\dfrac{\text{ctg}\alpha\cdot\text{ctg}\beta+1}{\text{ctg}\alpha-\text{ctg}\beta}$, $\alpha\neq nk$, $k\in Z$, $\beta\neq\pi m$, $m\in Z$, $\alpha-\beta\neq\pi n$, $n\in Z$.