AP Pre-Calculus Trigonometry Identities

Reciprocal, quotient, double angle, and sum and difference Pre-Calculus Trigonometric Identities.

tan x (quotient identity)

(sin x)/(cos x)

cot x (quotient identity)

(cosx)/(sinx)

sin²x+cos²x

1

1 + cot²x

csc²x

1+tan²x

sec²x

cos(A + B)

cosAcosB - sinAsinB

cos(A - B)

cosAcosB + sinAsinB

sin(A + B)

sinAcosB + sinBcosA

sin(A - B)

sinAcosB - sinBcosA

sin x

1/(csc x)

csc x

1/(sin x)

cos x

1/(sec x)

sec x

1/(cos x)

tan x (reciprocal identity)

1/(cot x)

cot x (reciprocal identity)

1/(tan x)

sin(2x) (expanded)

sinxcosx + sinxcosx

sin (2x) (simplified)

2sinxcosx

cos(2x) (expanded)

cosxcosx - sinxsinx

cos(2x) (simplified with both sine and cosine)

cos²x - sin²x

cos(2x) (simplified with only sine)

1 - 2sin²x

cos(2x) (simplified with only cosine)

2cos²x - 1