Trig Identities/Formulas

Reciprocal Identities

sinθ = 1/cscθ
cscθ = 1/sinθ

cosθ = 1/secθ
secθ = 1/cosθ

tanθ = 1/cotθ
cotθ = 1/tanθ

Quotient Identities

tanθ = sinθ/cosθ
cotθ = cosθ/sinθ

Pythagorean Identities

sin^2 x + cos^2 x = 1
tan^2 x + 1 = sec^2 x
cot^2 x + 1 = csc^2 x

Cofunction Identities

sin (pi/2 - x) = cos x
cos (pi/2 - x) = sin x

tan (pi/2 - x) = cot x
cot (pi/2 - x) = tan x

sec (pi/2 - x) = csc x
csc (pi/2 - x) = sec x

Even/Odd Identities

sin(-x) = - sin x
cos(-x) = cos x
tan (-x) = - tan x
csc (-x) = - csc x
sec (-x) = sec x
cot (-x) = - cot x

Sum & Difference Formulas

cos (x + y) = cos x cos y - sin x sin y
cos (x - y) = cos x cos y + sin x sin y

sin (x + y) = sin x cos y + cos x sin y
sin (x- y) = sin x cos y - cos x sin y

tan (x + y) = (tan x + tan y)/(1 - tan x tan y)
tan (x - y) = (tan x - tan y)/(1 + tan x tan y)

Double Angle Formulas

sin(2x) = 2sin(x)cos(x)
cos(2x) = cos^2(x) - sin^2(x); 2cos^2(x) - 1; 1 - 2sin^2(x)
tan(2x)=2tan(x)/1-tan^2 (x)