Question

5cos^2x+5cosx=1-3sin^2x

Answer 1

$5Cos^{2}x+5Cosx=1-3Sin^{2}x\\\\5Cos^{2}x+5Cosx=1-3(1-Cos^{2}x)\\\\5Cos^{2}x+5Cosx=1-3+3Cos^{2}x\\\\2Cos^{2}x+5Cosx+2=0\\\\Cosx=m;-1\leq m\leq 1\\\\2m^{2}+5m+2=0\\\\D=5^{2}-4*2*2=25-16=9=3^{2}\\\\m_{1}=\frac{-5+3}{4}=-\frac{1}{2}\\\\m_{2}=\frac{-5-3}{4}=-2<-1-neyd\\\\Cosx=-\frac{1}{2}\\\\x=\pm arc Cos(-\frac{1}{2})+2\pi n,n\in Z \\\\\boxed{x=\pm\frac{2\pi }{3}+2\pi n,n\in Z}$