wykazanie równości

[robin5hood]

Udowadni że jeśli \(\displaystyle{ \alpha, \beta,\gamma \in R-\{x:x=\frac{\pi}{2} + k \pi, k \in C \}}\) i \(\displaystyle{ \alpha+ \beta + \gamma= 0}\)

to \(\displaystyle{ ctg + ctg \beta + ctg \gamma = ctg *ctg \beta * ctg \gamma}\)

[mol_ksiazkowy]

Pojdzie ale z tg a nie ctg :

\(\displaystyle{ tg(\gamma) (tg\alpha \ tg\beta -1) - (tg\alpha+tg \beta) = -tg(\alpha + \beta) (tg\alpha \ tg\beta -1) - (tg\alpha+tg \beta) = 0}\)

gdyz

\(\displaystyle{ tg(\alpha + \beta ) = \frac{tg \alpha +tg \beta}{1- tg \alpha \ tg \beta}}\)