`cos 3x-cos 5x+sin x=0`
`<=>2sin 4x.sin x+sin x=0`
`<=>sin x(2sin 4x+1)=0`
`<=>[(sin x=0),(2sin 4x+1=0):}`
`<=>[(x=k\pi),(sin 4x=-1/2):}`
`<=>[(x=k\pi),([(4x=-\pi/6+k2\pi),(4x=[7\pi]/6+k2\pi):}):}`
`<=>[(x=k\pi),(x=-\pi/24+k\pi/2),(x=[7\pi]/24+k\pi/2):}` `(k in ZZ)`
\(\Leftrightarrow-2\cdot sin\left(\dfrac{3x-5x}{2}\right)\cdot sin\left(\dfrac{3x+5x}{2}\right)+sinx=0\)
\(\Leftrightarrow2sinx\cdot sin4x+sinx=0\)
\(\Leftrightarrow sinx\left(2sin4x+1\right)=0\)
=>x=kpi hoặc sin4x=-1/2
\(\Leftrightarrow\left[{}\begin{matrix}x=k\cdot pi\\4x=-\dfrac{pi}{6}+k2pi\\4x=\dfrac{7}{6}pi+k2pi\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=k\cdot pi\\x=-\dfrac{pi}{24}+\dfrac{kpi}{2}\\x=\dfrac{7}{24}pi+\dfrac{kpi}{2}\end{matrix}\right.\)
