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TRIGONOMETRIC FORMULAS
Trigonometric sign Functions
- sin (-θ) = − sin θ
- cos (−θ) = cos θ
- tan (−θ) = − tan θ
- cosec (−θ) = − cosec θ
- sec (−θ) = sec θ
- cot (−θ) = − cot
Periodic identities
- sin(2nπ + θ ) = sin θ
- cos(2nπ + θ ) = cos θ
- tan(2nπ + θ ) = tan θ
- cot(2nπ + θ ) = cot θ
- sec(2nπ + θ ) = sec θ
- cosec(2nπ + θ ) = cosec θ
Trigonometric identities
- sin2A + cos2A = 1
- tan2A + 1 = sec2A
- cot2A + 1 = cosec2A
Sum and Difference of two angles
- sin (A + B) = sin A cos B + cos A sin B
- sin (A − B) = sin A cos B – cos A sin B
- cos (A + B) = cos A cos B – sin 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)]
- tan(A – B) = [(tan A – tan B)/(1 + tan A tan B)]
Double Angle formulas
- sin 2A = 2 sin A cos A = [2 tan A /(1 + tan2A)]
- cos 2A = cos2A – sin2A = 1 – 2 sin2A = 2 cos2A – 1 = [(1 – tan2A)/(1 + tan2A)]
- tan 2A = (2 tan A)/(1 – tan2A)
Triple Angle formulas
- sin 3A = 3 sinA – 4 sin3A
- cos 3A = 4 cos3A – 3 cos A
- tan 3A = [3 tan A – tan3A]/[1 − 3 tan2A]