Question

Помогите доказать тождество

Answer 1

$\displaystyle \frac{\sin\alpha+\sin3\alpha+\sin5\alpha}{\cos\alpha+\cos3\alpha+\cos5\alpha}=\frac{2\sin3\alpha\cos2\alpha+\sin3\alpha}{2\cos3\alpha\cos2\alpha+\cos3\alpha}=\\ \\ \\ =\frac{\sin3\alpha(2\cos2\alpha+1)}{\cos3\alpha(2\cos2\alpha+1)}=\frac{\sin3\alpha}{\cos3\alpha}=\tt tg3\alpha$