c)
tg\alpha=\frac{\sqrt2}{2}
\frac{sin\alpha}{cos\alpha}=\frac{\sqrt2}{2}
2sin\alpha=\sqrt2cos\alpha
sin\alpha=\frac{\sqrt2cos\alpha}{2}
podstawiamy do wzoru na jedynkę
\frac{cos^2\alpha}{2}+cos^2\alpha=1 / *2
cos^2+2cos^2\alpha=2
3cos^2\alpha=2
cos\alpha=\sqrt{\frac{2}{3}}
cos\alpha=\frac{\sqrt2}{\sqrt3}*\frac{\sqrt3}{\sqrt3}=\frac{\sqrt6}{2}
sin\alpha=\frac{\sqrt2*0,5\sqrt6}{2}=0,25sqrt{12}=0,25*2\sqrt3=0,5\sqrt3