[tex]2\beta = \alpha+ \gamma[/tex]
[tex]2cos\gamma = \sqrt3 sin\alpha - cos\alpha[/tex]
Wyznaczam γ
[tex]\alpha+\beta+\gamma=180^o[/tex]
[tex]\beta=180^o-\alpha-\gamma[/tex]
[tex]2\beta = \alpha+ \gamma[/tex]
[tex]2(180^o-\alpha-\gamma) = \alpha+ \gamma[/tex]
[tex]360^o-2\alpha-2\gamma = \alpha+ \gamma[/tex]
[tex]360^o = \alpha+ \gamma+2\alpha+2\beta[/tex]
[tex]3\alpha+ 3\gamma=360^o\ \ \ |:3[/tex]
[tex]\alpha+ \gamma=120^o[/tex]
[tex]\gamma=120^o-\alpha[/tex]
[tex]2cos\gamma=2cos(120^o-\alpha)=2cos[180^o-(60^o+\alpha=-2cos(60^o+\alpha)=[/tex]
[tex]-2(cos60^ocos\alpha-sin60^o sin\alpha)=-2(\frac{1}{2}cos\alpha-\frac{\sqrt3}{2}sin\alpha)=[/tex]
[tex]-cos\alpha+\sqrt3sin\alpha= \sqrt3 sin\alpha - cos\alpha[/tex]