this should be fairly easy, but I'm afraid as I'm at a loss as on how to solve this.

sinx = cosx on an interval of 0 <= x < 2pi

I can reason it out... since sin is opposite over hypotenuse and cos is adjacent over hypotenuse, this is only true where adjacent = opposite, making it $\displaystyle \frac{\pi}{4}$ and $\displaystyle \frac{5\pi}{4}$.

But how is the problem solved algebraically?