Question

csc(theta/2)=sin(theta/2) find all solutions. and solutions in [0,2pi]

Answer 1

Let's think about sin(u)=csc(u)

Answer 2

when is sin(u) the same as it's reciprocal csc(u)?

Answer 3

We also want to solve on the interval theta [0,2pi]
that is
\[0 \le \theta \le 2 \pi \\ \text{dividing all sides by 2 gives } \\ 0 \le \frac{ \theta}{2} \le \pi\]
so solve sin(u)=csc(u) on the interval u [0,pi]

Answer 4

once you have found u
we will go back in find theta through the relation theta/2=u