Question

Решить уравнение cos2x+3sin^2x+3sinx*cosx=0

Answer 1

$cos2x+3sin^2x+3sin xcos x=0 \ cos^2x-sin^2x+3sin^2x+3sin xcos x=0 \ 2sin^2x+3sin xcos x+cos^2x=0 \ dfrac{2sin^2x}{cos^2x}+dfrac{3sin xcos x}{cos^2x}+dfrac{cos^2x}{cos^2x}=0 \ 2mathrm{tg}^2x+3mathrm{tg}x+1=0 \ mathrm{tg}x_1=-1 Rightarrow x_1=-dfrac{pi}{4}+pi n, ninZ \ mathrm{tg}x_2=-dfrac{1}{2} Rightarrow x_2=-mathrm{arctg}dfrac{1}{2} +pi n, ninZ$