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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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