solve 2tan(x/2)-cscx=0 for 0< or equal to (theta)<2pi

Question

I need help solving the equation

Answer 1

2tan(x/2)-cscx=0

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

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

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

2sin(x/2)-1/(2sin(x/2))=0, assuming cos(x/2)≠0

sin²(x/2)=1/4

a)sin(x/2)=1/2

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

I think you can solve equations a) and b) on your own.