# 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 = cos
^{2}x – sin^{2}x / 2cos^{2}x – 1 / 1-2sin^{2}x

### 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

- sin
^{2}x + cos^{2}x = 1 - 1+tan
^{2}x = sec^{2}x - 1+cot
^{2}x = cosec^{2}x

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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