$\begin{array}{l}
\,c{\rm{o}}{{\rm{s}}^3}x + {\sin ^3}x = \sin 2x + {\mathop{\rm s}\nolimits} {\rm{inx}} + \cos x\\
\Leftrightarrow (cosx+sinx)(1-cosxsinx)=sin2x+sinx+cosx \end{array}$
$\begin{array}{l}
\Leftrightarrow \left( {{\mathop{\rm s}\nolimits} {\rm{inx}} + \cos x} \right)\left( {1 - \cos
x\sin x - 1} \right) = 2\sin x\cos x\\
\Leftrightarrow 2\sin x\cos x + \sin {\rm{x}}\cos x({\mathop{\rm s}\nolimits} {\rm{inx}} +
\cos x) = 0\\
\Leftrightarrow \sin {\rm{x}}\cos x = 0 \Leftrightarrow \sin 2x = 0 \Rightarrow x = \frac{{k\pi }}{2} (k\in Z)
\end{array}$
(do PT
$\sin x+\cos x+2=0$ vô nghiệm)