Решите уравнение cos²5x+cos5x=2-sin²5x

cos^2(5x)+sin^2(5x)=1; 1+cos(5x)=2 cos(5x)=1 5x=2*n*pi x=2*5*pi*n

[latex]cos^25x + cosx5x = 2 - sin^25x \\ cos^25x + cos5x = 1 + cos^25x + sin^25x -sin^25x \\ cos5x = 1 \\ 5x = 2 \pi n, \ n \in Z \\ \boxed{x = \frac{2}{5} \pi n, \ n \in Z.}[/latex]