Question

Cos2x=2cosx-1 решите уравнение

Answer 1

$cos2x=2cosx-1$

$cos^2x-sin^2x=2cosx-1$

$cos^2x-(1-cos^2x)=2cosx-1$

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

$2cos^2x-2cosx=0$

$cosx(cosx-1)=0$

$cosx=0$

$x=frac{pi}{2} +pi n, nin Z$

$cosx=1$

$x=2pi n, nin Z$

Ответ: $2pi n, nin Z$ и $frac{pi}{2} +pi n, nin Z$