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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