Solve using identities [0,2) cos2x=sinx

We have:



Thus:



Adding gives:



Factoring gives:



Thus, we have:



or

.

Note that because , there will be no solutions of the form for positive integer and solution .  So we find the basic values of giving .

For with positive , (this can be seen easily from the unit circle.  But , a contradiction.  So we examine the case in which .

In this case, .  So this is the only solution to this equation.

Substituting this back in, we have , as desired.  So this is a valid solution.

Thus, .