Trigonometric Identities

cscθ

secθ

tanθ

cotθ

sin²θ

cos²θ

1

cot²θ

csc²θ

sec²θ

tan²θ

sinθ

1/cscθ

cosθ

1/secθ

secθ reciprocal identity

1/cosθ

cscθ reciprocal identity

1/sinθ

cotθ reciprocal identity

1/tanθ

tanθ quotient identity

sinθ/cosθ

cotθ quotient identity

cosθ/sinθ

-sinθ odd-even identity

sin(-θ)

cosθ odd-even identity

cos(-θ)

-tanθ odd-even identity

tan(-θ)

-cscθ odd-even identity

csc(-θ)

secθ odd-even identity

sec(-θ)

-cotθ odd-even identity

cot(-θ)

sinθ cofunction identity

cos (π/2-θ)

cosθ cofunction identity

sin (π/2-θ)

tanθ cofunction identity

cot (π/2-θ)

cscθ cofunction identity

sec (π/2-θ)

secθ cofunction identity

csc (π/2-θ)

cotθ cofunction identity

tan (π/2-θ)

sin²θ + cos²θ Pythagorean identity

1

1 + tan²θ Pythagorean identity

sec²θ

1 + cot²θ Pythagorean identity

csc²θ

sin(α + β) sum identity

sinαcosβ + cosαsinβ

sin(α - β) difference identity

sinαcosβ - cosαsinβ

cos(α + β) sum identity

cosαcosβ - sinαsinβ

cos(α - β) difference identity

cosαcosβ + sinαsinβ

tan(α + β) sum identity

tanα + tanβ/1 - tanαtanβ

tan(α - β) difference identity

tanα - tanβ/1 + tanαtanβ

sin 2θ double-angle identity

2 sinθcosθ

cos 2θ double-angle identity

cos²θ - sin²θ

2 cos²θ - 1

1 - 2 sin²θ

tan 2θ double-angle identity

2 tanθ/1 - tan²θ

sin½θ half-angle identity

±√1 - cosθ/2

cos½θ half-angle identity

±√1 + cosθ/2

tan½θ half-angle identity

±√1 - cosθ/1 + cosθ

1/sin x

csc x

1/cos x

sec x

1/tan x

cot x

1/csc x

sin x

1/sec x

cos x

1/cot x

tan x

sin²x+cos²x

1

1-cos²x

sin²x

1-sin²x

cos²x

1+tan²x

sec²x

1+cot²x

csc²x

sec²x-1

tan²x

csc²x-1

cot²x

sin(-x)

-sin x

csc(-x)

-csc x

cos(-x)

cos x

sec(-x)

sec x

tan(-x)

-tan x

cot(-x)

-cot x

sin(π/2-x)

cos x

cos(π/2-x)

sin x

tan(π/2-x)

cot x

csc(π/2-x)

sec x

sec(π/2-x)

csc x

cot(π/2-x)

tan x

sin x / cos x

tan x

cos x/ sin x

cot x