Question

2sin^2x=cos x +1..................

Answer 1

$2sin^2x=cos x+1\2-2cos^2x=cos x+1\2cos^2x+cos x-1=0\cos x=t,;cos^2x=t^2,;tin[-1;;1]\2t^2+t-1=0\D=1+4cdot2=9\t_1=-1,;t_2=frac12\cos x=-1Rightarrow x=pi+2pi n\cos x=frac12Rightarrow x=fracpi3+2pi n,;ninmathbb{Z}$