Question

Решите выражение:

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

Answer 1

$2cos^2x-cos^2x+2cosx-1=0$
$cos^2x+2cosx-1=0$
$cosx=t,te[-1;1]$
$t^2+2t-1=0$
$D=4+4=8$
$t_1=\frac{-2+\sqrt8}2=\frac{2(-1+\sqrt2)}2=-1+\sqrt2$
$t_2=\frac{-2-2\sqrt2}2=-1-\sqrt2\ \textless \ -1$
$cosx=-1+\sqrt2$
$x=+-arccos(-1+\sqrt2)+2\pi n;n\in Z$