Question

$frac{2sin2a + cos( frac{3pi}{2} - a ) - sin (pi + a) }{1 + sin ( frac{3pi}{2} - a)}$

Answer 1

$frac{2sin2 alpha + cos( frac{3 pi }{2} - alpha ) - sin ( pi + alpha ) }{1 + sin ( frac{3 pi }{2} - alpha )} = frac{2sin2 alpha -sin alpha + sin alpha }{1 - cos alpha} = frac{2sin2 alpha }{1 - cos alpha} =$$= frac{2sin2 alpha }{2sin^2 frac{ alpha }{2} } =frac{sin2 alpha }{sin^2 frac{ alpha }{2} } =frac{2sin alpha cos alpha }{sin^2 frac{ alpha }{2} } =frac{2*2sin frac{ alpha }{2} cos frac{ alpha }{2} cos alpha }{sin^2 frac{ alpha }{2} } = frac{4cos frac{ alpha }{2}cos alpha }{sin frac{ alpha }{2} } =$$=4ctg frac{ alpha }{2}cos alpha$