Question

Решите:
cos^2x=1/2(1-cosx)

Answer 1

$Cos^{2}x=frac{1-Cosx}{2}\\Cos^{2}x-frac{1-Cosx}{2}=0 \\2Cos^{2}x-1+Cosx=0\\2Cos^{2}x+Cosx-1=0\\Cosx=m,-1 leq m leq 1 \\2m^{2}+m-1=0\\D=1^{2} -4*2*(-1)=1+8=9=3^{2}\\m_{1}=frac{-1+3}{4}=frac{1}{2} \\m_{2} =frac{-1-3}{4}=-1\\Cosx=frac{1}{2}\\x=+-arcCosfrac{1}{2}+2pi n,nez\\x=+-frac{pi }{3}+2pi n,nez\\Cosx=-1\\x=pi +2pi n,nez$