[tex]\big(1-\cos\alpha\big)\big(\frac1{\sin\alpha}+\frac1{\text{tg\,}\alpha}\big)-\sin\alpha=0\\\\\\ L=\big(1-\cos\alpha\big)\big(\frac1{\sin\alpha}+ \frac1{\text{tg\,}\alpha}\big)-\sin\alpha= \big(1-\cos\alpha\big)\big(\frac1{\sin\alpha} + \frac{\cos\alpha}{\sin\alpha}\big)-\sin\alpha= \\\\= \big(1-\cos\alpha\big)\cdot \frac{1+\cos\alpha}{\sin\alpha}-\sin\alpha=\frac{1-\cos^2\alpha}{\sin\alpha}-\sin\alpha=\frac{\sin^2\alpha}{\sin\alpha}-\sin\alpha=\\\\=\sin\alpha-\sin\alpha=0=P[/tex]
