IM3H TRIG IDENTITIES

[Fundamental] sin^2 θ + cos^2 θ

1

[Sum & Difference] sin(A + B)

sin A cos B + cos A sin B

[Sum & Difference] sin(A - B)

sin A cos B - cos A sin B

[Sum & Difference] cos(A + B)

cos A cos B - sin A sin B

[Sum & Difference] cos(A - B)

cos A cos B + sin A sin B

[Sum & Difference] tan(A + B)

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

[Sum & Difference] tan(A - B)

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

[Double-Angle] sin(2A)

2 sin A cos A

[Double-Angle 1] cos(2A)

cos^2 A - sin^2 A

[Double-Angle 2] cos(2A)

2 cos^2 A - 1

[Double-Angle 3] cos(2A)

1 - 2 sin^2 A

[Double-Angle] tan(2A)

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

[Half-Angle] sin(A/2)

±√((1 - cos A)/2)

[Half-Angle] cos(A/2)

±√((1 + cos A)/2)

[Half-Angle 1] tan(A/2)

sin A/(1 + cos A)

[Half-Angle 2] tan(A/2)

(1 - cos A)/sin A

[Half-Angle 3] tan(A/2)

±√((1 - cos A)/(1 + cos A))

[Pythagorean] 1 + tan^2 θ

sec^2 θ

[Pythagorean] 1 + cot^2 θ

csc^2 θ

[Cofunction] sin(90° - θ)

cos θ

[Cofunction] cos(90° - θ)

sin θ

[Cofunction] tan(90° - θ)

cot θ

[Cofunction] cot(90° - θ)

tan θ

[Cofunction] sec(90° - θ)

csc θ

[Cofunction] csc(90° - θ)

sec θ

[Reciprocal] sin θ

1/csc θ

[Reciprocal] cos θ

1/sec θ

[Reciprocal] tan θ

1/cot θ

[Reciprocal] csc θ

1/sin θ

[Reciprocal] sec θ

1/cos θ

[Reciprocal] cot θ

1/tan θ

[Quotient] cot θ

cos θ / sin θ