Question

cos 4x= cos 12x 

Answer 1

`cos 4x=cos 12x`

`<=>` $\left[\begin{matrix} 4x=12x+k2\pi\\ 4x=-12x+k2\pi\end{matrix}\right.$  `(k in ZZ)`

`<=>` $\left[\begin{matrix} 8x=-k2\pi\\ 16x=k2\pi\end{matrix}\right.$  `(k in ZZ)`

`<=>` $\left[\begin{matrix} x=\dfrac{-k\pi}{4}\\ x=\dfrac{k\pi}{8}\end{matrix}\right.$  `(k in ZZ)`

Answer 2

\(\Leftrightarrow\left\{{}\begin{matrix}4x=12x+k2\Pi\\4x=-12x+k2\Pi\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-k\Pi}{8}\\x=\dfrac{k\Pi}{16}\end{matrix}\right.\)