Question

cos(\(\dfrac{\pi}{5}-2x\))=\(\dfrac{4}{5}\)

Answer 1

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{\Pi}{5}-2x=arccos\left(\dfrac{4}{5}\right)+k2\Pi\\\dfrac{\Pi}{5}-2x=-arccos\left(\dfrac{4}{5}\right)+k2\Pi\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x=\dfrac{\Pi}{5}-arccos\left(\dfrac{4}{5}\right)-k2\Pi\\2x=\dfrac{\Pi}{5}+arccos\left(\dfrac{4}{5}\right)-k2\Pi\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{\Pi}{10}-arccos\left(\dfrac{4}{5}\right):2-k\Pi\\x=\dfrac{\Pi}{10}+arccos\left(\dfrac{4}{5}\right):2-k\Pi\end{matrix}\right.\)