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Trigonometric Identities

The list of the formulae below can be helpful when helping students to prove some simple trigonometric identities.

Double Angle Formulas

  • sin2x = 2sinxcosx
  • cos2x = cos2x – sin2x / 2cos2x – 1 / 1-2sin2x

Reciprocal Identities

  • sin x = 1/cosec x
  • cos x = 1/sec x
  • tan x = 1/cot x

Quotient Identities

  • tanx = sinx/cosx
  • cotx = cosx/sinx

    Pythagorean Identities

    • sin2x + cos2x = 1
    • 1+tan2x = sec2x
    • 1+cot2x = cosec2x

    Which can be derived from Pythagoras’ Theorem.

    Sum and Difference formulas

    • sin(x+y) = sin x(cos y) + cos x(sin y)
    • cos(x+y) = cos x(cos y) – sin x(sin y)
    • sin(x-y) = sin x(cos y) – cos x(sin y)
    • cos(x-y) = cos x(cos y) + sin x(sin y)

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