Răspuns:
Fie [tex]\alpha=18^{\circ}[/tex]
Avem
[tex]90^{\circ}=5\alpha=2\alpha+3\alpha\Rightarrow 2\alpha=90-3\alpha\Rightarrow\sin 2\alpha=\cos 3\alpha\Rightarrow\\\Rightarrow 2\sin\alpha\cos\alpha=4\cos^3\alpha-3\cos\alpha\Rightarrow 4\cos^2\alpha-2\sin\alpha-3=0\Rightarrow\\\Rightarrow4\sin^2\alpha+2\sin\alpha-1=0\Rightarrow\sin\alpha=\displaystyle \frac{-1+\sqrt{5}}{4}[/tex]
Atunci
[tex]\cos\alpha=\sqrt{1-\sin^2\alpha}=\displaystyle\frac{\sqrt{10+2\sqrt{5}}}{4}[/tex]
Explicație pas cu pas:
