AP Precalculus - Trig Identities

Sin Odd/Even

sin(-x)= -sinx

Cos Odd/Even

cos(-x)=cosx

Tan Odd/Even

tan(-x) = -tanx

Csc Odd/Even

csc(-x)= -cscx

Sec Odd/Even

sec(-x)=secx

Cot Odd/Even

cot(-x)= -cotx

Sin Sum

sin(x+y)=sinxcosy+cosxsiny

Sin Difference

sin(x-y)=sinxcosy-sinycosx

Cos Sum

cos(x+y)=cosxcosy-sinxsiny

Cos Difference

cos(x-y)=cosxcosy+sinxsiny

Tan Sum

\frac{\tan x+\tan y}{1-\tan x\tan y}=\tan\left(x+y_{}\right)

Tan Difference

\tan\left(x-y\right)=\frac{\tan x-\tan y}{1+\tan x\tan y}

Sin Double Angle

sin2x=2sinxcosx

Cos Double Angle

cos2x=

• cos²x-sin²x

• 1-2sin²x

• 2cos²x-1

Tan Double Angle

\tan2x=\frac{2\tan x}{1-\tan^2}