precalc trig identities

(angle sum identity) sin(x + y) =

sin(x)cos(y) + sin(y)cos(x)

(angle sum identity) cos(x + y) =

cos(x)cos(y) - sin(x)sin(y)

(angle sum identity) tan(x + y) =

(tan(x) + tan(y)) / (1 - tan(x)tan(y))

(angle difference identity) sin(x - y) =

sin(x)cos(y) - sin(y)cos(x)

(angle difference identity) cos(x - y) =

cos(x)cos(y) + sin(x)sin(y)

(angle difference identity) tan(x - y) =

(tan(x) - tan(y)) / (1 + tan(x)tan(y))

(double angle identity) sin2x =

2sin(x)cos(x)

(double angle identity) cos2x =

cos²(x) - sin²(x) OR 2cos²(x) - 1 OR 1 - 2sin²(x)

(double angle identity) tan2x =

(2 tan(x)) / (1 - tan²(x))

(power reducing identity) sin²x =

(1 - cos2x) / 2

(power reducing identity) cos²x =

(1 + cos2x) / 2

(power reducing identity) tan²x =

(1 - cos2x) / (1+ cos2x)

(half-angle identity) sin(x/2) =

+- √((1 - cosx) / 2)

(half-angle identity) cos(x/2) =

+- √((1 + cosx) / 2)

(half-angle identity) tan(x/2) =

(1 - cosx) / sinx OR sinx / (1 + cosx)