Trig Identities

Pythagorean Identites

1. cos^2t+ sin^2t =1 2. 1+ tan^2t=sec^2t 3. Cot^2t +1= csc^2t

Difference/ Sum identities for cosine

Cos (α-β)=cosαcosβ+ sinαsinβ Cos (α+β)= cosαcosβ-sinαsinβ

Even-Odd Identites

Cos(-t)=cost Sin(-t)= -sint Tan(-t)= -tant Sec (-t)= sect Csc (-t)= -csct Cot(-t)= -cott

Difference/sum identities for sine

Sin (α-β)=sinαcosβ-sinβcosα Sin (α+β)=sinαcosβ+sinβcosα

Double Angle Identites

Sin(2x)= 2sinxcosx Cos(2x)= cos^2x-sin^2x =1-2sin^2x =2cos^2x-1 Tan(2x)= 2tanx/1-tan^2x

Periodic identities

Sin(t+- 2nπ)=sint cos(t+-2nπ)=cost tan(t+-nπ)=tant

Reciprocal identities

Sint= 1/csct cott= 1/tant cost= 1/sect csct= 1/sint tant= 1/cott sect= 1/cost

Quotient Identites

Tant= sint/cost cott= cost/sint

Half-Angle Identites

cos(x/2)= +- square root of 1+cosx/2 sin(x/2)= +- square root of 1-cosx/2 Tan(x/2)= +- square root of 1-cosx/ 1+cosx

Difference/sum identites for tangent

tan (α-β)=tanα-tanβ/1+tanαtanβ Tan (α+β) = tanα+tanβ/1-tanαtanβ