Question

2 cos^2 x - cos x - 1 = 0

Answer 1

$2 cos^{2}x-cosx-1=0; \ cosx=t; \ 2 t^{2} -t-1=0; \ D=1+8=9; \ t_{1} = frac{1+3}{4}=1; \ t_{2}= frac{1-3}{4}=- frac{1}{2}; \ cosx=1; x=2 pi n; \ cosx=- frac{1}{2} ;x= frac{ pi }{3}+2 pi n; \ Answer: x= frac{ pi }{3}+2 pi n; x=2 pi n;$