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 sin
 cos
 ;
cos(α) + cos(β) = 2 cos
cos
;
sin(α) - sin(β) = 2 cos
sin
;
cos(α) - cos(β) = - 2 sin
sin
|
| 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) = 
.
|
