Решете tan(alpha+beta)-tanalpha-tanbeta/tanalphatan(alpha+beta)=tanbeta

$$\frac { \tan ( \alpha + \beta ) - \tan \alpha - \tan \beta } { \tan \alpha \tan ( \alpha + \beta ) } = \tan \beta$$

Реши за α

$$\alpha \notin \frac{\pi n_{2}}{2},\frac{\pi n_{2}}{2}-\beta$$

$$\forall n_{2}\in \mathrm{Z}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\beta =\pi n_{1}+\frac{\pi }{2}$$

Реши за β

$$\beta \notin \frac{\pi n_{2}}{2}-\alpha ,\pi n_{2}+\frac{\pi }{2}$$

$$\forall n_{2}\in \mathrm{Z}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\alpha =\frac{\pi n_{1}}{2}$$