Question

Помогите решить

cos^2 5x=5cos 5x

Answer 1

$cos^25x=5cos5x\\cos^25x-5cos5x=0\\cos5x(cos5x-5)=0\\left[begin{array}{ccc}cos5x=0\cos5x-5=0end{array}rightquadrightarrowquadleft[begin{array}{ccc}displaystyle 5x=frac{pi}2+pi n;,,nin Z\cos5x=5end{array}rightquadrightarrow\\\left[begin{array}{ccc}displaystyle x=frac{pi}{10}+frac{pi n}{5};,,nin Z\\varnothingquadend{array}rightquadrightarrowquadboxed{x=frac{pi}{10}+frac{pi n}{5};,,nin Z}$