Trig Identities

Pythagorean Identities

sin²θ + cos²θ = 1
tan²θ + 1 = sec²θ
cot²θ + 1 = csc²θ

Quotient identities

sin²θ + cos²θ = 1
tan²θ + 1 = sec²θ
cot²θ + 1 = csc²θ

Co-Function identities

sin(-θ) = -sinθ

cos(-θ) = cosθ

tan(-θ) = -tanθ

Odd/Even identities

sin(-θ) = -sinθ

cos(-θ) = cosθ

sin(π/2 – θ) = cosθ

cos(π/2 – θ) = sinθ

Periodicity identities

sin(θ + 2π) = sinθ

cos(θ + 2π) = cosθ

tan(θ + π) = -tanθ

Double angle identities

sin 2θ = 2sinθcosθ

cos 2θ = cos²θ – sin²θ

tan 2θ = (2tanθ)/(1 – tan²θ)

Half angle identities

sin(θ/2) = ±√[(1 – cosθ)/2]

cos(θ/2) = ±√[(1 + cosθ)/2]

tan(θ/2) = ±√[(1 – cosθ)/(1 + cosθ)]

Product-to-Sum identities

sin(A + B) = sinAcosB + cosAsinB

sin(A – B) = sinAcosB – cosAsinB

cos(A + B) = cosAcosB – sinAsinB

cos(A – B) = cosAcosB + sinAsinB

Note: θ represents an angle in the unit circle and A, B are angles. The ± sign represents both positive and negative square root solutions.