tg\alpha=2
tg\alpha=\frac{sin\alpha}{cos\alpha}
2=\frac{sin\alpha}{cos\alpha}/*cos\alpha
2cos\alpha=sin\alpha/:2
cos\alpha=\frac{sin\alpha}{2}
sin^2\alpha+cos^2\alpha=1
sin^2\alpha+(\frac{sin\alpha}{2})^2=1
sin^2\alpha+\frac{sin^2\alpha}{4}=1/*4
4sin^2\alpha+sin^2\alpha=4
5sin^2\alpha=4
sin^2\alpha=\frac{4}{5}
sin\alpha=\sqrt{\frac{4}{5}}
sin\alpha=\frac{2}{\sqrt5}=\frac{2*\sqrt5}{\sqrt5*\sqrt5}
sin\alpha=\frac{2\sqrt5}{5} odpowiedź D