[latex] \frac{sin2 \alpha }{1-cos2 \alpha }* \frac{1-cos \alpha }{cos \alpha } [/latex]

[latex]1-cos2 \alpha =2sin^2 \alpha [/latex] [latex]sin2 \alpha =2sin \alpha *cos \alpha [/latex] [latex] \frac{sin2 \alpha }{1-cos2 \alpha } * \frac{1-cos \alpha }{cos \alpha } = \frac{2sin \alpha *cos \alpha }{2sin^2 \alpha } * \frac{1-cos \alpha }{cos \alpha }= \frac{cos \alpha }{sin \alpha }* \frac{1-cos \alpha }{cos \alpha }= \frac{1-cos \alpha }{sin \alpha }= [/latex][latex]\frac{2sin^2 \frac{ \alpha }{2} }{2sin \frac{ \alpha }{2}*cos \frac{ \alpha }{2} }= \frac{sin \frac{ \alpha }{2} }{cos \frac{ \alpha }{2} } =tg \frac{ \alpha }{2} [/latex]