Trigonify

Double Angle

Double angle formula: cos 2θ in all three forms

cos⁡2θ=cos⁡2θ−sin⁡2θ=2cos⁡2θ−1=1−2sin⁡2θ\cos 2\theta = \cos^{2}\theta - \sin^{2}\theta = 2\cos^{2}\theta - 1 = 1 - 2\sin^{2}\theta

cos 2θ has three equivalent forms: cos²θ − sin²θ, 2cos²θ − 1, and 1 − 2sin²θ. The Pythagorean identity converts between them. Pick whichever leaves you with only the function you already have - that choice is usually what makes a problem fall out in one line instead of five.

Related Double Angle identities

sin 2θtan 2θ

Practise it

Reading a formula is not the same as recalling it under time pressure. The workspace drills Double Angle questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.

Practise Double AngleOpen the triangle solver

Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.