Trigonometric Identities

Reciprocal sinx

1/cscx

Reciprocal cscx

1/sinx

Reciprocal cosx

1/secx

Reciprocal secx

1/cosx

Reciprocal tanx

1/cotx

Reciprocal cotx

1/tanx

1 coat in the closet

1 + cot^2x = csc^2x

I tan in one second

1 + tan^2x = sec^2x

1 =

sin^2x + cos^2x

Quotient tanx

sinx/cosx

Quotient cotx

cosx/sinx

sin(-x)

-sinx

csc(-x)

-cscx

cos(-x)

cosx

sec(-x)

secx

tan(-x)

-tanx

cot(-x)

-cotx

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

cos^2x-sin^2x, 2cos^x-1, 1-2sin^2x

tan2x

(2tanx)/(1-tan^2x)

sin(A/2)

±√ (1-cosA)/2

cos(A/2)

±√ (1+cosA)/2

tan(A/2)

±√ (1-cosA)/(1+cosA) = (sinA)/(1+cosA) = (1-cosA)/sinA