Question

помогите решить задание на фото

Answer 1

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)