Упростить tga(1+cos2a)

[latex]\tan\alpha(1+\cos2 \alpha )=\tan\alpha(\cos^2\alpha+\sin^2 \alpha+\cos^2\alpha-\sin^2 \alpha)=[/latex] [latex]=\tan\alpha*2\cos^2\alpha=2\tan\alpha*\cos^2\alpha=2 \frac{\sin \alpha \cos^2\alpha}{\cos\alpha}= 2\sin\alpha \cos\alpha=[/latex] [latex]=\sin2\alpha[/latex]