Question

cos2x=2cosx-1 решите уравнение

Answer 1

Cos2x-2Cosx+1=0. Cos^2x-Sin^2x-2Cosx+1=0. Cos^2x-1+Cos^2x-2Cosx+1=0. 2Cos^2x-2Cosx=0. 2Cosx(Cosx-1)=0. Cosx=0 и Cosx=1. x=П/2+Пn и x=0+2Пn, где n€Z