SSC SSC-Maths Trigonometry

Theory : Trigonometry

Trigonometric Identities and Formulas

There are three systems of measuring Angles-

1. Circular System

  • Unit of Measurement is radian.
  • 180 degree = π radians

2. Sexagesimal System (English System)

  • Right angle is divided into 90 equal parts called degree.
  • Unit of Measurement is degree.
  • Each degree is divided into 60 equal parts called minute. (1 degree = 60’)
  • Each minute divided into 60 equal parts called seconds (1 minute = 60’’)

3. Centesimal or French System

  • Right angle is divided into 100 equal parts.
  • Unit of measurement is grades.
  • Each grade is divided into 100 equal parts called minute, and minutes into seconds.

Sign Conventions

  • cos (90 – θ) = sinθ
  • tan (90 – θ) = cotθ
  • cosec (90 – θ) = secθ
  • sec (90 – θ) = cosecθ
  • cot (90 – θ) = tanθ

Some Basic Formulas and Identities

  1. sin2θ + cos2θ = 1
  2. 1 + tan2θ = sec2θ
  3. 1 + cot2θ = cosec2θ
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Advanced Trigonometric Identities

  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)
  7. cot (A + B) = (cot A cot B – 1) / (cot A + cot B)
  8. cot (A – B) = (cot A cot B + 1) / (cot B – cot A)
  9. sin 2θ = 2sinθcosθ
  10. sin2θ = 2tanθ/1+tan2θ
  11. cos2θ = 2cos2θ – 1
  12. cos2θ = cos2θ – sin2θ
  13. cos2θ = 1 – 2sin2θ
  14. cos2θ = (1 – tan2θ)/( 1 + tan2θ)
  15. tan2θ = 2tanθ/1 – tan2θ
  16. sin3θ = 3sinθ – 4sin3θ
  17. cos3θ = 4cos3θ – 3cosθ
  18. tan3θ = (3tanθ – tan3θ)/(1 – 3tan2θ)
  19. tan (A + B + C) = (tan A + tan B + tan C – tan A tan B tan C)/(1 – tan A tan B – tan B tan C – tan C tan A)
  20. 2sin A sin B = cos (A – B) – cos (A + B)
  21. 2cos A cos B = cos (A + B) + cos (A – B)
  22. 2sin A cos B = sin (A + B) + sin (A – B)
  23. 2cos A sin B = sin (A + B) – sin (A – B)
  24. sinC + sinD = 2sin[(C + D)/2] × cos[(C – D)/2]
  25. sinC – sinD = 2cos[(C + D)/2] × sin[(C – D)/2]
  26. cosC + cosD = 2cos[(C + D)/2]cos[(C – D)/2]
  27. cosC – cosD = 2sin[(C + D)/2]cos[(D – C)/2]
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