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$Z$