trigonometric identities

Reciprocal Identities (6)

sinθ = 1/cscθ ; cscθ = 1/sinθ

cosθ = 1/secθ ; secθ = 1/cosθ

tanθ = 1/cotθ ; cotθ = 1/tanθ

ratio identities (2)

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

pythagorean Identities (3)

sin^2θ+cos^2θ=1

1+tan^2θ=sec^2θ

1+cot^2θ=csc^2θ

complement Identities (6)

sin π/2-θ = cos θ; csc π/2-θ = sec θ

cos π/2-θ = sin θ; sec π/2-θ = csc θ

tan π/2-θ = cot θ; tan π/2-θ = θ

supplementary identities (6)

sin π-θ = sin θ; csc π-θ = csc θ

cos π-θ = - cos θ; sec π-θ = - sec θ

tan π-θ = - tan θ; cot π-θ = -cot θ

even odd identities (6)

sin(-θ) = -sin θ; csc(-θ) = -csc θ

cos (-θ) = cos θ; sec (-θ) = -sec θ

tan (-θ) = -tan θ; cot (-θ) = -cot θ

sin (a+b)

sinacosb + sinbcosa

cos (a+b)

cosacosb - sinasinb

tan (a+b)

tana + tanb/1-tanatanb

sin (a-b)

sinacosb - sinbcosa

cos (a-b)

cosacosb + sinasinb

tan (a-b)

tana - tan b/ 1 + tanatanb

sin (2θ)

2sinθcosθ

cos (2θ)

cos^2 θ - sin^2 θ

1 - 2sin^2 θ

2cos^2 θ - 1

tan (2θ)

2tan θ/1 - tan^2θ

sin (θ/2)

±⎷1 - cos θ/2

cos (θ/2)

±⎷1+cos θ/2

tan

±⎷1 - cos θ /1 + cos θ