Доказать тождество. tg(a)+ctg(a)=2/sin2a

[latex]tg \alpha+ctg\alpha=\frac{sin\alpha}{cos\alpha}+\frac{cos\alpha}{sin\alpha}=\frac{sin^2\alpha}{sin\alpha \cos\alpha}+\frac{cos^2\alpha}{sin\alpha \cos\alpha} = \\ =\frac{sin^2\alpha+cos^2\alpha}{sin\alpha \cos\alpha}=\frac{1}{\frac{1}{2}\cdot2sin\alpha \cos\alpha}=\frac{1}{\frac{1}{2}sin2\alpha}=\frac{2}{sin2\alpha}[/latex]