Question

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

Answer 1

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