Trigonometric Identities for AP Precalculus

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

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

sin 2θ double-angle identity

2 sinθcosθ

cos 2θ double-angle identity

cos²θ - sin²θ

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 / cos x

tan x

cos x/ sin x

cot x