Other Formula

It is clear that one can play many games using DeMoivre's (Euler's) Theorem, when it comes to needing a specialized formula for a special reason. As an example, we are often required to integrate something like

$$\int \sin^2\theta d \theta$$

or

$$\int \sin \theta \cos \theta d \theta$$

over a domain. These integrals are often handled by replacing the sines and cosines by exponetials using you know what, and expanding the polynomial, regrouping, and then either integrating directly, or recovering simple sines and cosines and then integrating, whichever seems simpler and/or more straightforward.