Question

ctg a * sin a/1-(sin a + cos a)^2

Answer 1

$ctgalpha*frac{sinalpha}{1-(sinalpha+cosalpha)^2} = frac{cosalpha}{sinalpha}*frac{sinalpha}{1 - (1+2sinalpha cosalpha)} = -frac{cosalpha}{2sinalpha cosalpha} = -frac1{2sinalpha}$