Cos(2a) = cos^2(a) - sin^2(a)
sin(2a) = 2*sin(a) * cos(a)
1 = cos^2(a) + sin^2(a)
подставляем и раскрываем скобки
cos^2(a) + sin^2(a) - cos^2(a) + sin^2(a) +2*sin(a) * cos(a)
--------------------------------------------------------------------------------
cos^2(a) + sin^2(a) + cos^2(a) + sin^2(a) +2*sin(a) * cos(a)
упрощаем
sin^2(a) + sin(a)*cos(a)
--------------------------------
cos^2(a) + sin(a)*cos(a)
Делим на cos^2(a)
tg(a) = 1/ctg(a)
tg^2(a) + tg(a)
------------------- = ( 9 + 1)/ (3 + 1) = 10/4 = 2.5
1 + tg(a)