Quotient Identities
tan(θ) sin(θ)/cos(θ)
cot(θ) cos(θ)/sin(θ)


Pythagorean Identities
sin2(θ) + cos2(θ) 1
sec2(θ) - tan2(θ) 1
csc2(θ) - cot2(θ) 1


Cofunction Identities
sin(π/2 - θ) cos(θ)
cos(π/2 - θ) sin(θ)
tan(π/2 - θ) cot(θ)
cot(π/2 - θ) tan(θ)
csc(π/2 - θ) sec(θ)
sec(π/2 - θ) csc(θ)


Double Angle Identities
sin(2θ) 2sin(θ)cos(θ)
cos(2θ) cos2(θ) - sin2(θ)
cos(2θ) 2cos2(θ) - 1
cos(2θ) 1 - 2sin2(θ)
tan(2θ) 2tan(θ)/[1 - tan2(θ)]


Sum to Product of Two Angles
sin(θ) + sin(ϕ) 2sin((θ + ϕ)/2)cos( (θ - ϕ)/2)
sin(θ) - sin(ϕ) 2cos((θ + ϕ)/2)sin( (θ - ϕ)/2)
cos(θ) + cos(ϕ) 2cos((θ + ϕ)/2)cos( (θ - ϕ)/2)
cos(θ) - cos(ϕ) -2sin((θ + ϕ)/2)sin( (θ - ϕ)/2)


Reciprocal Identities
sin(θ) 1/csc(θ)
cos(θ) 1/sec(θ)
tan(θ) 1/cot(θ)
csc(θ) 1/sin(θ)
sec(θ) 1/cos(θ)
cot(θ) 1/tan(θ)


Even/Odd Identities
sin(-θ) -sin(θ)
cos(-θ) cos(θ)
tan(-θ) -tan(θ)
csc(-θ) -csc(θ)
sec(-θ) sec(θ)
cot(-θ) -cot(θ)


Sum/Difference Identities
sin(θ ± ϕ) sin(θ)cos(ϕ) ± cos(θ)sin(ϕ)
cos(θ ± ϕ) cos(θ)cos(ϕ) ∓ sin(θ)sin(ϕ)
tan(θ ± ϕ) [tan(θ) ± tan(ϕ)]/[1 ∓ tan(θ)tan(ϕ)]


Half Angle Identities
sin2(θ) [1 - cos(2θ)]/2
cos2(θ) [1 + cos(2θ)]/2
tan2(θ) [1 - cos(2θ)]/[1 + cos(2θ)]


Product to Sum of Two Angles
sin(θ)sin(ϕ) [cos(θ - ϕ) - cos(θ + ϕ)]/ 2
cos(θ)cos(ϕ) [cos(θ - ϕ) + cos(θ + ϕ)]/ 2
sin(θ)cos(ϕ) [sin(θ + ϕ) + sin(θ - ϕ)]/ 2
cos(θ)sin(ϕ) [sin(θ + ϕ) - sin(θ - ϕ)]/ 2