Question

Cosx+cos3x-sin4x=0

Answer 1

P/t \(\Leftrightarrow2cos2x.cosx-2.sin2x.cos2x=0\)

\(\Leftrightarrow cos2x\left(cosx-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cos2x=0\\cosx=1\end{matrix}\right.\)  \(\Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{\pi}{2}+k\pi\\x=2k\pi\end{matrix}\right.\)  ( k \(\in Z\) )

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}\\x=2k\pi\end{matrix}\right.\)