Stim urmatoarele
[tex]tgx=\frac{\sin{x}}{\cos{x}}[/tex]
[tex]ctgx=\frac{\cos{x}}{\sin{x}}[/tex]
[tex]\sin{2x}=2\sin{x}\cos{x}[/tex]
Atunci
[tex]\frac{\sin{x}}{\cos{x}}+\frac{\cos{x}}{\sin{x}}=\frac{\sin^{2}{x}+\cos^{2}{x}}{\sin{x}\cos{x}}=\frac{1}{\sin{x}\cos{x}}=\frac{2}{2\sin{x}\cos{x}}=\frac{2}{\sin{2x}}=\frac{5}{\sqrt{3}}\Rightarrow \sin{2x}=\frac{2\sqrt{3}}{5}[/tex]
