Double angle formula: cos 2θ in all three forms
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
Common questions
What is the cos 2θ identity?
cos 2θ has three equivalent forms: cos²θ − sin²θ, 2cos²θ − 1, and 1 − 2sin²θ. The Pythagorean identity converts between them.
When do you use the cos 2θ identity?
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.
Which identities are related to cos 2θ?
cos 2θ belongs to the Double Angle group. The identities used alongside it most often are sin 2θ and tan 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.
Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.