Compound & multiple angles

The cosine of a sum or difference of two angles is found using $\cos (A\pm B)=\cos A\cos B\mp \sin A\sin B$. These identities let you evaluate trigonometric functions for angles built from standard angles such as $30^{\circ }$, $45^{\circ }$, and $60^{\circ }$. Repeated use of the sum formulas also produces multiple-angle formulas, such as $\cos 3\theta =4{\cos }^3\theta -3\cos \theta$.