I was asked to solve the following equation:

I solved it by changing the csc(x) to and then by multiplying through by sin(x), yielding:

I then used the "completing the square" method to solve the equation and arrived at sin(x) = 1. Because I ended up with such a neat answer, I'm wondering if I missed some easier way to solve the problem.

Was there a more simple way I could have solved this that wouldn't have involved completing the square or using the quadratic equation?

Thanks!