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Trigonometric Identities

Trignometric functions of Class 11

  • Sin nπ = 0 if n∈I
  • Cos nπ/2 = 0 if n is an odd integer
  • cos (nπ + θ) = (-1)n cos θ, n ∈ I
  • sin (nπ + θ) = (-1)n sin θ, n ∈ I
  • Cos (nπ/2 +θ) = (−1)(n + 1)/2 Sinθ, if n is odd integer
  • Sin (nπ/2 +θ) = (−1)(n-1/2) Cosθ, if n is odd integer

For Any Three Angles A,B,C

(a) sin (A+B+C) = sin A cos B cos C + sin B cos C cos A + sin C cos A cos B − sin A sin B sin C

(b) cos (A+B+C) = cos A cos B cos C – cos A sin B sin C - cos B sin A sin C – cos C sin A sin B

(c) tan (A+B+C) = Trigonometric Identities

(d) cot (A+B+C) = Trigonometric Identities

Greatest And Least Values of a cosθ + b sinθ

Trigonometric Identities

Some Important Identities

If A+B+C = π then

  1. sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C
  2. cos 2A + cos 2B + cos 2C = -1 –4 cos A cos B cos C
  3. sin A + sin B + sin C = 4 CosA/2 cos B/2 cosC/2
  4. cos A + cos B + cos C = 1 + 4 sin A/2 sin B/2 sin C/2
  5. tan A + tan B + tan C = tan A tan B tan C
  6. cot A cot B + cot B cot C + cot C cot A = 1
  7. tan A/2 tan B/2 + tan B/2 tan C/2 + tan C/2 tan A/2 = 1
  8. cot A/2 + cot B/2 + cot C/2 = cot A/2. cot B/2. cot C/2

Two Useful Identities

  1. cos α + cos β + cos γ + cos (α+β+γ) = 4 Trigo
  2. sin α + sin β + sin γ - sin (α+β+γ) = 4 Trigo
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