Question

Помогите решить тригонометрическое уравнение!

Answer 1

$ctg( frac{x}{2})-tg( frac{x}{2})-2tg(x)=4 \ frac{sin x}{1-cos x} - frac{sin x}{1+cos x} - frac{2sin x}{cos x}=4 \ \ dfrac{sin x+sin xcos x-sin x+cos xsin x}{sin^2x} - frac{2sin x}{cos x} =4 \ \ 2ctg x-2tg x=4 \ tg^2x+2tg x-1=0 \ D=8 \ tg x= -2pm sqrt{2} \ x=arctg(-2pm sqrt{2})+ pi n,n in Z$