Cosine sum and difference formula: cos(α ± β) = cos α cos β ∓ sin α sin β
cos(α ± β) = cos α cos β ∓ sin α sin β. The signs are opposite: a plus inside gives a minus outside. That sign flip is the most commonly dropped detail in the whole topic, and it comes from cosine being even while sine is odd.
Related Sum & Difference identities
Common questions
What is the cos(α ± β) identity?
cos(α ± β) = cos α cos β ∓ sin α sin β. The signs are opposite: a plus inside gives a minus outside.
When do you use the cos(α ± β) identity?
That sign flip is the most commonly dropped detail in the whole topic, and it comes from cosine being even while sine is odd.
Which identities are related to cos(α ± β)?
cos(α ± β) belongs to the Sum & Difference group. The identities used alongside it most often are sin(α ± β) and tan(α ± β).
Practise it
Reading a formula is not the same as recalling it under time pressure. The workspace drills Sum & Difference 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.