Обчислити ctg7pi/12

Ответ: -2+1,5√3.

Пошаговое объяснение:

ctg (7π/12)=ctg(π-5π/12)= - ctg(5π/12)= -ctg(2π/12+3π/12) =

= - ctg(π/6+π/4)= - 1/ tg(π/6+π/4)= - (1-tg π/6*tg π/4):( tg π/6+tg π/4)=

= (√3/3 * 1 - 1):(√3/3+1) = (√3/3 -1)(√3/3-1) : ((√3/3+1)(√3/3-1)) =

= (1/3-√3+1):(1/3-1) = (4/3-√3)*(-3/2) = -2+1,5√3.