Phương trình tương đương với:$\sin x+\frac{1}{2}(\sin3x+\sin x)-\sqrt{3}\cos 3x=2(\cos 5x+\sin^3x)$$\Leftrightarrow \frac{3}{2}\sin x-2\sin^3x+\frac{1}{2}\sin 3x-\sqrt{3}\cos 3x=2\cos 5x$ $\Leftrightarrow
\frac{1}{2}\sin 3x +
\frac{1}{2}\sin 3x -\sqrt{3}
\cos 3x=2\cos 5x $ $\Leftrightarrow
\frac{1}{2}\sin 3x -\frac{\sqrt{3}}{2} \cos 3x=\cos 5x $ $\Leftrightarrow \sin\Big(3x-\frac{\pi}{3}\Big)=\sin\Big(\frac{\pi}{2}- 5x\Big)$ $\Leftrightarrow \left[ \begin{array}{l} 3x-\frac{\pi}{3}=\frac{\pi}{2}-5x+2k\pi\\3x- \frac{\pi}{3}=5x+\frac{\pi}{2}+2k\pi \end{array} \right. (k\in\mathbb{Z})$$\Leftrightarrow \left[ \begin{array}{l} x=\frac{5\pi}{48}+\frac{k}{4}\pi\\ x=\frac{-5\pi}{12}-k\pi \end{array} \right. (k\in\mathbb{Z})$
Phương trình tương đương với:$\sin x+\frac{1}{2}(\sin3x+\sin x)-\sqrt{3}\cos 3x=2(\cos 5x+\sin^3x)$$\Leftrightarrow \frac{3}{2}\sin x-2\sin^3x+\frac{1}{2}\sin 3x-\sqrt{3}\cos 3x=2\cos 5x$ $\Leftrightarrow
\frac{1}{2}\sin 3x +
\frac{1}{2}\sin 3x -\sqrt{3}
\cos 3x=2\cos 5x $ $\Leftrightarrow
\frac{1}{2}\sin 3x -\frac{\sqrt{3}}{2} \cos 3x=\cos 5x $ $\Leftrightarrow \sin\Big(3x-\frac{\pi}{3}\Big)=\sin\Big(\frac{\pi}{2}- 5x\Big)$ $\Leftrightarrow \left[ \begin{array}{l} 3x-\frac{\pi}{3}=\frac{\pi}{2}-5x+2k\pi\\
\frac{\pi}{3}-3x=5x+\frac{\pi}{2}+2k\pi \end{array} \right. (k\in\mathbb{Z})$$\Leftrightarrow \left[ \begin{array}{l} x=\frac{5\pi}{48}+\frac{k}{4}\pi\\ x=\frac{-\pi}{48}-\frac{k}{4}\pi \end{array} \right. (k\in\mathbb{Z})$
Phương trình tương đương với:$\sin x+\frac{1}{2}(\sin3x+\sin x)-\sqrt{3}\cos 3x=2(\cos 5x+\sin^3x)$$\Leftrightarrow \frac{3}{2}\sin x-2\sin^3x+\frac{1}{2}\sin 3x-\sqrt{3}\cos 3x=2\cos 5x$ $\Leftrightarrow
\frac{1}{2}\sin 3x +
\frac{1}{2}\sin 3x -\sqrt{3}
\cos 3x=2\cos 5x $ $\Leftrightarrow
\frac{1}{2}\sin 3x -\frac{\sqrt{3}}{2} \cos 3x=\cos 5x $ $\Leftrightarrow \sin\Big(3x-\frac{\pi}{3}\Big)=\sin\Big(\frac{\pi}{2}- 5x\Big)$ $\Leftrightarrow \left[ \begin{array}{l} 3x-\frac{\pi}{3}=\frac{\pi}{2}-5x+2k\pi\\
3x- \frac{\pi}{3}=5x+\frac{\pi}{2}+2k\pi \end{array} \right. (k\in\mathbb{Z})$$\Leftrightarrow \left[ \begin{array}{l} x=\frac{5\pi}{48}+\frac{k}{4}\pi\\ x=\frac{-
5\pi}{
12}-k\pi \end{array} \right. (k\in\mathbb{Z})$