Cos 2 альфа, если tg (альфа-2 П/3) = 2-корень из3

Tg (a-2π/3) = (tga-tg2π/3) / (1+tga*tg2π/3) = (tga+√3/2) / (1-√3/2tga) = 2-√3

tga+√3/2 = (1-√3/2tga) * (2-√3)

tga+√3/2=2-√3-√3tga+3/2

tga+√3tga=2-√3+3/2-√3/2

tga (1+√3) = (7/2-3√3/2)

tga = (7/2-3√3/2) / (1+√3) = (7/2-3√3/2) * (√3-1)) / (3-1) = (7/4-3√3/4) (√3-1) =

=7√3/4-7/4-9/4+3√3/4) = 10√3/4-4=2,5√3-4

cos²a=1: (1+tg²a) = 1: (1+18,75-20√3+16) = 1 / (35,75-20√3)

cos2a=2cos²a-1=2 / (35,75-20√3) - 1 = (2-35,75+20√3) / (35,75-20√3=

= (-33,75+20√3) / (35,75-20√3)