Sum and Difference Identities

sin (x + π) ≠ sin x + sin π Cannot distribute Cosine of a difference (proof) cos (u-v) = cos u cos v + sin u sin v

Identities

Sine of a Sum

sin (u+v) = sin u cos v + cos u sin v

Sine of a Difference

sin (u-v) = sin u cos v - cos u sin v

Cosine of a Sum

cos (u+v) = cos u cos v - sin u sin v

Cosine of a Difference

cos (u-v) = cos u cos v + sin u sin v

Tangent of a Sum

tan (u+v) = (tan u + tan v)/(1-tan u tan v)

Tangent of a Difference

tan (u-v) = (tan u - tan v)/(1+ tan u tan v)

When to use it:

Example:

cos(15) = cos (45-30)