Solve for x: sin x = cos (2x + 15)
I'll just add a bit of background:
$\displaystyle \sin x = \cos \left(\frac{\pi}{2} - x \right)$ and so the equation can be written as $\displaystyle \cos \left(\frac{\pi}{2} - x \right) = \cos (2x + 15)$.
Now you need to understand the symmetry of the unit circle: $\displaystyle \cos A = \cos B$ means that either $\displaystyle A = B + 2 n \pi$ or $\displaystyle A = -B + 2 n \pi$ where n is an integer.