Identities are equations that are true for all values of the variables involved.This lesson is meant to summarize the various identities that are used in relation to Trigonometry.
| Quotient | Reciprocol | Pythagorean | Compound Angle |
| \(\tan\theta = \cfrac{\sin\theta}{\cos\theta}\) | \(\csc\theta = \cfrac{1}{\sin\theta}\) | \(\sin²\theta + \cos²\theta = 1\) | \(\sin(x+y) = \sin(x)\cos(y) + \cos(x)\sin(y)\) |
| \(\cot\theta = \cfrac{\cos\theta}{\sin\theta}\) | \(\sec\theta = \cfrac{1}{\cos\theta}\) | \(\sec²\theta - \tan²\theta = 1\) | \(\sin(x-y) = \sin(x)\cos(y) - \cos(x)\sin(y)\) |
| \(\cot\theta = \cfrac{1}{\tan\theta}\) | \(\csc²\theta + \cot²\theta = 1\) | \(\cos(x+y) = \cos(x)\cos(y) - \sin(x)\sin(y)\) | |
| \(\cos(x-y) = \cos(x)\cos(y) + \sin(x)\sin(y)\) |