Question

$frac{sin2 alpha }{1-cos2 alpha }* frac{1-cos alpha }{cos alpha }$

Answer 1

$1-cos2 alpha =2sin^2 alpha$

$sin2 alpha =2sin alpha *cos alpha$


$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 }=$$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}$