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 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(2nÏ€ + 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(B) = [(tan tan B)/(– tan tan B)]
  6. tan(A – B) = [(tan A – tan B)/(1 + tan 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]



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