trig functions

cos(A+B)

cosAcosB-sinAsinB

cos(A-B)

cosAcosB+sinAsinB

sin(A+B)

sinAcosB+cosAsinB

sin(A-B)

sinAcosB-cosAsinB

tan(A+B)

tanA+tanB/1-tanAtanB

tan(A-B)

tanA-tanB/1+tanAtanB

sin2x

2sinxcosx

cos2x (with both cos and sin)

cos^2x-sin^2x

cos2x (with sin only)

1-2sin^2x

cos2x (with cos only)

2cos^2x-1

tan2x

2tanx/1-tan^2x

sin^2x+cos^2x

1

sin^2x

1-cos^2x

cos^2x

1-sin^2x

tan^2x

sec^2x-1

sec^2x

1+tan^2x

cot^2x+1

csc^2x

cot^2x

csc^2x-1

sec^2x-tan^2x

1

csc^2x-cot^2x

1

cos (x/2) Half Angle formula

±√((1 + cos x)/2)

sin(x/2) (half-angle)

±√((1 − cos x)/2)

Express tan(x/2) with square root

±√((1 − cos x)/(1 + cos x))

Express tan(x/2) in terms of sin x and cos x.

tan(x/2) = sin x/(1 + cos x) = (1 − cos x)/sin x

secx (reciprocal identity)

1/cosx

cscx (reciprocal identity)

1/sinx

cotx (reciprocal identity)

1/tanx

tanx (quotient identity)

sinx/cosx

cotx (quotient identity)

cosx/sinx

cos(-x)

cosx

sin(-x)

-sinx

tan(-x)

-tanx

sec(-x)

secx

csc(-x)

-csc(x)

cot(-x)

-cotx

tan(pi/2-x)

cot(x)

sin(pi/2-x)

cosx

cos(pi/2 - x)

sinx

cot(pi/2-x)

tan x

sec(pi/2-x)

csc x

csc(pi/2 - x)

secx