Geometry & Trigonometry
Intermediate

Cosine Double Angle

Double-angle identity for cosine.

Formula

cos⁡(2θ)=cos⁡2θ−sin⁡2θ\cos(2\theta) = \cos^2\theta - \sin^2\theta

Variables

\thetaAngle

Example

cos 60° = cos²30° − sin²30° = 3/4 − 1/4 = 1/2. ✓

Did You Know?

This identity has three equivalent forms — pick whichever cancels the terms you have.

trigonometryidentitydouble angle