This is what the problem says:
solve the equation for solutions in the interval [0,2pi]
showing all steps would be appreciated.
2sin²(x) - cos(x) - 1 = 0
I solved it this way:
Since , then
substitute in your equation and you get
using distributive and reordering terms you get
Now you have to make a change of variables, so let , then (you will need this later)
and substituting in this last equation you get
which has roots and
Then and or
Those are the 3 solutions