Yes, what you did is the way to go.
The question is solve on the interval
using the identity
I can't factor that, so I completed the square and got.
It looks like that will give me the solutions, but I've never completed the square on a trigonometric function before and just wanted to check that it's the right way to proceed.
If you are solving for x there is another useful identity: the double angle formula.
As long as we agree that cos(x) is not zero we may cancel one of the cosine terms:
Now, 2 sin(x) cos(x) = sin(2x). Thus
And go from there. I get that