Hello

I am struggling with a simple trig equation, again.

The question is to solve, on the interval ,

Using my graphing calculator I get four solutions.

Dividing through by I get:

, for which there are only two solutions. Two of the four I should have.

I have come across this before, where decreasing the power reduces the number of solutions, which makes sense, although I don't understand it. I'd by grateful if someone would explain where I'm going wrong.

Thank you