Question

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

Answer 1

$ctg\alpha*\frac{sin\alpha}{1-(sin\alpha+cos\alpha)^2} = \frac{cos\alpha}{sin\alpha}*\frac{sin\alpha}{1 - (1+2sin\alpha cos\alpha)} = -\frac{cos\alpha}{2sin\alpha cos\alpha} = -\frac1{2sin\alpha}$