[tex]sin^{2}x + cos^{2}x = 1 \ \ \rightarrow \ \ sin^{2}x = 1 - cos^{2}x[/tex]
[tex]L = 2\cdot tgx\cdot cos x = 2\cdot\frac{sinx}{cosx}\cdot cosx = 2sinx\\\\P = \frac{1-cos^{2}x}{sinx}+sinx = \frac{sin^{2}x}{sinx}+sinx = sinx + sin x = 2sinx\\\\L = P[/tex]
