AP Precalculus Trig Identities

sin²θ + cos²θ

1

1 + tan²θ

sec²θ

1 + cot²θ

csc²θ

sin(-u), csc(-u)

-sin(u), -csc(u)

cos(-u), sec(-u)

cos(u), sec(u)

tan(-u), cot(-u)

-tan(u), -cot(u)

π/2 - θ relationships

sin-cos, csc-sec, tan-cot

sin(u+v)

sinucosv + cosusinv

sin(u-v)

sinucosv - cosusinv

cos(u+v)

cosucosv - sinusinv

cos(u-v)

cosucosv + sinusinv

tan(u+v)

(tanu + tanv) / (1 - tanutanv)

tan(u-v)

(tanu - tanv) / (1 + tanutanv)

sin2θ

2sinθcosθ

cos2θ

cos²θ-sin²θ

cos2θ

2cos²θ-1

cos2θ

1-2sin²θ

tan2θ

(2tanθ)/(1 - tan²θ)

sin(θ/2)

±sqrt((1-cosθ)/2))

cos(θ/2)

±sqrt((1+cosθ)/2))

tan(θ/2)

±sqrt((1-cosθ)/(1+cosθ))

tan(θ/2)

((1-cosθ)/sinθ)

tan(θ/2)

(sinθ)/(1+cosθ))