Sin 15 a-sina+sin7a/cos 15 a+cosa+cos7a

[latex] \frac{\sin15 \alpha-\sin\alpha+\sin7\alpha }{\cos15\alpha+\cos\alpha+\cos7\alpha} = \frac{ 2\sin \frac{15\alpha-\alpha}{2}\cos \frac{15\alpha+\alpha}{2} +\sin7\alpha}{2\cos \frac{15\alpha+\alpha}{2}\cos \frac{15\alpha-\alpha}{2}+\cos7\alpha }= \\ \\ = \frac{2\sin7\alpha\cos8\alpha+\sin7\alpha}{2\cos8\alpha\cos7\alpha+\cos7\alpha} = \frac{\sin7\alpha(2\cos8\alpha+1)}{\cos7\alpha(2\cos8\alpha+1)}= \frac{\sin7\alpha}{\cos7\alpha}=tg7\alpha [/latex]