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| 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 sin   cos   ;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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