Ответ: 2

Объяснение:

[tex]\displaystyle (\mathrm {tg} x+\mathrm {ctg} x ) \cdot \sin 2x = \bigg ( \frac{\sin x}{\cos x} +\frac{\cos x}{\sin x} \bigg ) \cdot 2\sin x \cos x = \\\\\\ \frac{\sin ^2x+\cos^2x }{\sin x\cdot \cos x } \cdot 2\sin x \cos x = \frac{1}{\sin x\cdot \cos x } \cdot 2\sin x \cos x = \boxed{2}[/tex]