Trig Identities

sin²θ + cos²θ

1

1 + tan²θ

sec²θ

1 + cot²θ

csc²θ

sinθ

1 / cscθ

cosθ

1 / secθ

tanθ

1 / cotθ

sin2θ

2sinθcosθ

cos2θ

cos²θ - sin²θ or 2cos²θ - 1 or 1- 2sin²θ

tan2θ

2tanθ / 1 - tan²θ

sin(A ± B)

sinAcosB ± cosAsinB

cos(A ± B)

cosAcosB ∓ sinAsinB

tan(A ± B)

tanA ± tanB / 1 ∓ tanAtanB

tanθ

sinθ / cosθ

cotθ

cosθ / sinθ

sin(−θ)

−sinθ

cos(−θ)

cosθ

tan(−θ)

−tanθ

cos(-x)

cos x

sin(-x)

-sin x

tan(-x)

-tan x

cot(-x)

-cot x

sec(-x)

sec x

csc(-x)

-csc x

cos(pi + x)

-cos x

cos(pi - x)

-cos x

sin(pi + x)

-sin x

sin(pi - x)

sin x

tan(pi + x)

tan x

tan(pi - x)

-tan x

cot(pi + x)

cot x

cot(pi - x)

-cot x

cos(pi/2 + x)

-sin x

cos(pi/2 - x)

sin x

sin(pi/2 + x)

cos x

sin(pi/2 - x)

cos x

tan(pi/2 + x)

-cot x

tan(pi/2 - x)

cot x

cot(pi/2 + x)

-tan x

cot(pi/2 - x)

tan x

cos(3pi/2 + x)

sin x

cos(3pi/2 - x)

-sin x

sin(3pi/2 + x)

-cos x

sin(3pi/2 - x)

-cos x

tan(3pi/2 + x)

cot x

tan(3pi/2 - x)

-cot x

cot(3pi/2 + x)

tan x

cot(3pi/2 - x)

-tan x

cos(2pi - x)

cos x

sin(2pi - x)

-sin x

tan(2pi - x)

-tan x