TRIGONOMETRIC FORMULAS

Trigonometric sign Functions

1. sin (-θ) = − sin θ
2. cos (−θ) = cos θ
3. tan (−θ) = − tan θ
4. cosec (−θ) = − cosec θ
5. sec (−θ) = sec θ
6. cot (−θ) = − cot 

Periodic identities 

1. sin(2nπ + θ ) = sin θ
2. cos(2nπ + θ ) = cos θ
3. tan(2nπ + θ ) = tan θ
4. cot(2nπ + θ ) = cot θ
5. sec(2nπ + θ ) = sec θ
6. cosec(2nπ + θ ) = cosec θ 

Trigonometric identities

1. sin2A + cos2A = 1
2. tan2A + 1 = sec2A
3. cot2A + 1 = cosec2A

Sum and Difference of two angles

1. sin (A + B) = sin A cos B + cos A sin B
2. sin (A − B) = sin A cos B – cos A sin B
3. cos (A + B) = cos A cos B – sin A sin B
4. cos (A – B) = cos A cos B + sin A sin B
5. tan(A + B) = [(tan A + tan B)/(1 – tan A tan B)]
6. tan(A – B) = [(tan A – tan B)/(1 + tan A tan B)]

Double Angle formulas

1. sin 2A = 2 sin A cos A = [2 tan A /(1 + tan2A)]
2. cos 2A = cos2A – sin2A = 1 – 2 sin2A = 2 cos2A – 1 = [(1 – tan2A)/(1 + tan2A)]
3. tan 2A = (2 tan A)/(1 – tan2A)

Triple Angle formulas

1. sin 3A = 3 sinA – 4 sin3A
2. cos 3A = 4 cos3A – 3 cos A
3. tan 3A = [3 tan A – tan3A]/[1 − 3 tan2A]