Solving trig equations

Question

I am struggling with how to get started for these problems.

Problem 1: 2sin^2 (x/2) -sin (x/2) = 0

Problem 2: csc^2 (x) -4csc (x) = 0

Answer 1

Factor out common factor!

1) (sin (x/2))(2 sin (x/2) - 1) = 0

2) (csc x)(csc x - 4) = 0

Now use Zero Product Rule.