1. Zadatak

Podijelimo li brojnik i nazivnik s $\cos(x/2)$ dobivamo

$$\frac{5-3\tg(x/2)}{3\tg(x/2)+2}=\frac{15}{13}$$

odakle slijedi $\tg(x/2)=5/12$.

Tada je $\cos(x/2)=12/13$ pa je

$$\tg(x/4)=\sqrt{\frac{1-\cos(x/2)}{1+\cos(x/2)}}=\sqrt{\frac{1/13}{25/13}}=\frac15.$$