Question

Giải phương trình sau :

             \(\cos3x-\cos5x=\sin x\)

Answer 1

\(\cos3x-\cos5x=\sin x\Leftrightarrow\sin x\left(1-2\sin4x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sin x=0\\\sin4x=\dfrac{1}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=k\pi,k\in\mathbb{Z}\\x=\dfrac{\pi}{24}+k\dfrac{\pi}{2},k\in\mathbb{Z}\\x=\dfrac{5\pi}{24}+k\dfrac{\pi}{2},k\in\mathbb{Z}\end{matrix}\right.\)