(1-cosa) /sina = tg(a/2) Доказать равенство

[latex] frac{1-cos alpha }{sin alpha } = 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]