sin^2(x) + cos^2(x) = 1

tan(x) = sin(x)/cos(x)

sec^2(x) = 1 + tan(x)

csc^2(x) = 1 + cot^2(x)

sec(x) = 1/cos(x)

csc(x) = 1/sin(x)

cot(x) = 1/tan(x) = cos(x)/sin(x)

Addtion and subtraction formulas:

sin(A + B) = sinAcosB + sinBcosA

sin(A - B) = sinAcosB - sinBcosA

cos(A + B) = cosAcosB - sinAsinB

cos(A - B) = cosAcosB + sinAsinB

tan(A + B) = (tanA + tanB)/(1 - tanAtanB)

tan(A - B) = (tanA - tanB)/(1 + tanAtanB)

the tan formulas are not as important to memorize, you can use the identity tan(x) = sin(x)/cos(x) to find them if necessary

Double angle formulas:

for these, you just apply the addtion formulas for two angles being the same.

sin(2A) = sin(A + A) = sinAcosA + sinAcosA = 2sinAcosA

cos(2A) = cos(A + A) = cosAcosA - sinAsinA = cos^2(A) - sin^2(A)

remember, sin^2(A) + cos^2(A) = 1

so sin^2(A) = 1 - cos^2(A) and,

cos^2(A) = 1 - sin^2(A)

so cos(2A) = 1 - sin^2(A) - sin^2(A) = 1 - 2sin^2(A)

or cos(2A) = cos^2(A) - (1 - cos^2(A)) = 2cos^2(A) - 1

tan(2A) = 2tanA/(1 - tan^2(A))