The given trigonometry equation is,
[tex]\frac{1}{\sin\theta}=2\cos \theta[/tex]
We are to get the solution under the interval 0 to 2pi. I will be resolving it graphically.
The graph is shown below
The solution to the equations on the graph is always where the two equations intersect each other on the graph.
Hence, from the graph we can obseved that they intersect each other at two points under the interval 0 to 2pi.
The two points are,
[tex](\frac{\pi}{4},\frac{5\pi}{4})[/tex]
Therefore, the solution is
[tex](\frac{\pi}{4},\frac{5\pi}{4})[/tex]
