Ctg(x/2) - tg(x/2) - 2tg(x) = 4 

Тождество для применения: [latex]tgx = \frac{2tg\frac{x}{2}}{1-tg^2\frac{x}{2}}[/latex]   [latex]\frac{1}{tg\frac{x}{2}}-tg\frac{x}{2}-2tgx=4[/latex] [latex]\frac{1-tg^2\frac{x}{2}}{tg\frac{x}{2}}-2tgx=4[/latex] [latex]\frac{2}{tgx}-2tgx-4=0[/latex] [latex]-tg^2x-2tgx+1=0 (tgx\neq0)[/latex]   tgx=a -a²-2a+1=0 a₁= -1+√2, a₂=-1-√2 tgx = -1+√2 ⇔ x = arctg(-1+√2)+πk, k∈Z tgx = -1-√2 ⇔ x = arctg(-1-√2)+πk, k∈Z