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SparkNotes Math Study Guides More Trigonometric Identities Formulae
 
Multiple Angles and Functions
 
 
Formulae
 
 
Double and Half-Angle Formulas
 
 
Problems
 
 
Addition and Subtraction Formulas
 
 
Problems
 
 
Products of Functions
 
 
Problems
 
 
Sums and Differences of Functions
 
 
Problems
 
 
 
 
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More Trigonometric Identities

 
 

Formulae

 
 
Addition of Angles sin(α + β) = sin(α)cos(β) + cos(α)sin(β); cos(α + β) = cos(α)cos(β) - sin(α)sin(β); tan(α + β) =
 
Double Angle sin(2x) = 2 sin(x)cos(x); cos(2x) = cos2(x) - sin2(x) = 1 - 2 sin2(x) = 2 cos2(x) - 1; tan(2x) =
 
Function Products sin(α)sin(β) = - (cos(α + β) - cos(α - β)); cos(α)cos(β) = (cos(α + β) + cos(α - β)); sin(α)cos(β) = (sin(α + β) + sin(α - β)); cos(α)sin(β) = (sin(α + β) - sin(α - β))
 
Function Sums and Differences sin(α) + sin(β) = 2 sincos; cos(α) + cos(β) = 2 coscos; sin(α) - sin(β) = 2 cossin; cos(α) - cos(β) = - 2 sinsin
 
Half Angle sin() = ±; cos() = ±; tan() = ± = =
 
Subtraction of Angles sin(α - β) = sin(α)cos(β) - cos(α)sin(β); cos(α - β) = cos(α)cos(β) + sin(α)sin(β); tan(α - β) = .
 
 
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