Question

Помогите решить

cos^2 5x=5cos 5x

Answer 1

$\cos^25x=5\cos5x\\\\\cos^25x-5\cos5x=0\\\\\cos5x(\cos5x-5)=0\\\\\left[\begin{array}{ccc}\cos5x=0\\\cos5x-5=0\end{array}\right\quad\rightarrow\quad\left[\begin{array}{ccc}\displaystyle 5x=\frac{\pi}2+\pi n;\,\,n\in Z\\\cos5x=5\end{array}\right\quad\rightarrow\\\\\\\left[\begin{array}{ccc}\displaystyle x=\frac{\pi}{10}+\frac{\pi n}{5};\,\,n\in Z\\\\\varnothing\quad\end{array}\right\quad\rightarrow\quad\boxed{x=\frac{\pi}{10}+\frac{\pi n}{5};\,\,n\in Z}$