Question

1-cosx=sinx*sinx/2 (x-деленное на 2) решите уравнение

Answer 1

$1-cosx=sinx *sin frac{x}{2} \ 1-cosx=sinx * sqrt{frac{1-cosx}{2}} \ (1-cosx) ^{2} =sin^{2}x*(frac{1-cosx}{2}) \ 1-cosx=frac{1-cos^2x}{2} \ cos^2x-2cosx+1=0 \ (cosx-1)^2=0 \ cosx-1=0 \ cosx=1 \ x=2 pi n, n in Z$