Math Trigonometric Identities

sin θ

1/csc θ

cos θ

1/sec θ

tan θ

1/cot θ

csc θ

1/sin θ

sec θ

1/cos θ

cot θ

1/tan θ

tan θ

sin θ / cos θ

cot θ

cos θ / sin θ

sin² θ + cos² θ

1

tan² θ + 1

sec² θ

cot² θ + 1

csc² θ

sin θ

cos(π/2 - θ)

csc θ

sec(π/2 - θ)

cos θ

sin(π/2 - θ)

sec θ

csc(π/2 - θ)

tan θ

cot(π/2 - θ)

cot θ

tan(π/2 - θ)

sin(-θ)

-sin θ

csc(-θ)

-csc θ

cos(-θ)

cos θ

sec(-θ)

sec θ

tan(-θ)

-tan θ

cot(-θ)

-cot θ

sin(A + B)

sin A * cos B + cos A * sin B

cos(A + B)

cos A * cos B - sin A * sin B

tan(A + B)

(tan A + tan B) / (1 - tan A * tan B)

sin(A - B)

sin A * cos B - cos A * sin B

cos(A - B)

cos A * cos B + sin A * sin B

tan(A - B)

(tan A - tan B) / (1 + tan A * tan B)

sin 2θ

2 sin θ * cos θ

cos 2θ

cos² θ - sin² θ

cos 2θ

1 - 2 sin² θ

cos 2θ

2 cos² θ - 1

tan 2θ

(2 tan θ) / (1 - tan² θ)

sin (θ/2)

±√((1 - cos θ) / 2)

cos (θ/2)

±√((1 + cos θ) / 2)

tan (θ/2)

±√((1 - cos θ) / (1 + cos θ))

tan (θ/2)

(1 - cos θ) / sin θ

tan (θ/2)

sin θ / (1 + cos θ)

sin² θ

(1 - cos 2θ) / 2

cos² θ

(1 + cos 2θ) / 2

tan² θ

(1 - cos 2θ) / (1 + cos 2θ)

sin A * sin B

(1/2)[cos(A - B) - cos(A + B)]

cos A * cos B

(1/2)[cos(A - B) + cos(A + B)]

sin A * cos B

(1/2)[sin(A + B) + sin(A - B)]

cos A * sin B

(1/2)[sin(A + B) - sin(A - B)]

sin A + sin B

2 sin((A + B) / 2) * cos((A - B) / 2)

cos A + cos B

2 cos((A + B) / 2) * cos((A - B) / 2)

sin A - sin B

2 cos((A + B) / 2) * sin((A - B) / 2)

cos A - cos B

-2 sin((A + B) / 2) * sin((A - B) / 2)