Finding all exact solutions to the equation on [0, 2pi)
2(cos^2)x + 3sinx = 3
I would suggest rewriting this using the fact that $\displaystyle \cos^2 x + \sin^2 x = 1$. From there you can treat $\displaystyle \sin x$ as a variable and solve the quadratic that results. If you don't understand the second part just post what you have after using the first suggestion.