Question

1+cos x = ctg x/2
Решить уравнение

Answer 1

$1+cos x=ctg frac{x}{2} \ 1+cos x= frac{1+cos x}{sin x} \ sin x(1+cos x)-(1+cos x)=0 \ (1+cos x)(sin x-1)=0 \ left[begin{array}{ccc}cos x=-1\sin x=1end{array}rightto left[begin{array}{ccc}x_1= pi +2 pi n,n in Z\ x_2= frac{ pi }{2}+2 pi k, k in Z end{array}right$