Simplifying trigonometric expressions can be helpful when we are solving trigonometric equations or proving trigonometric identities. We can use the basic trigonometric ratios, combined and double-angle formulas, as well as reciprocal and other identities to do so.

The following are common formulas and identities we can use as tools to simplify trigonometric expressions:

(Source: https://www.onlinemathlearning.com/image-files/trigonometric-identities.png)

Watch this video for proofs of the Pythagorean Identities:

You can use the information on the following image to remember the combined angle formulas: