Pythagorean Identities
\sin^2(\theta) + \cos^2(\theta) = 1
\tan^2(\theta) + 1 = \sec^2(\theta)
\cot^2(\theta) + 1 = \csc^2(\theta)
Reciprocal Identities
\sec(\theta) = \frac{1}{\cos(\theta)}
\csc(\theta) = \frac{1}{\sin(\theta)}
\cot(\theta) = \frac{1}{\tan(\theta)}
Quotient Identities
\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}
\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}
Co-function Identities (Complimentary angles)
\sin\left(\frac{\pi}{2} - \theta\right) = \cos(\theta)
\cos\left(\frac{\pi}{2} - \theta\right) = \sin(\theta)
\tan\left(\frac{\pi}{2} - \theta\right) = \cot(\theta)
\sec\left(\frac{\pi}{2} - \theta\right) = \csc(\theta)
\csc\left(\frac{\pi}{2} - \theta\right) = \sec(\theta)
\cot\left(\frac{\pi}{2} - \theta\right) = \tan(\theta)