Доказать: tg[latex] \alpha [/latex]+ctg[latex] \alpha [/latex]=[latex] \frac{2}{sin2 \alpha } [/latex]

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