Half-Angle Formulas

Formulas expressing trigonometric functions of an angle  x/2  in terms of functions of an angle x.

sin(1/2x) = + [(1 - cos x) / 2]-2

cos(1/2x) = + [(1 + cos x) / 2]-2

tan(1/2x) = + [(1 - cos x) / (1 + cos x)]-2

tan(1/2x) = [1 + (1 + tan2 x)-2 ] / tan x

tan(1/2x) = (sin x) / (1 + cos x)

tan(1/2x) = (1 - cos x) / sin x

tan(1/2x) = (tan x  sin x) / (tan x + sin x)