$\begin{array}{l}
1)pt \Leftrightarrow \sin \left( {3x - {{15}^0}} \right) = \frac{{\sqrt 3 }}{2}\\
\Leftrightarrow \left[ \begin{array}{l}
3x - {15^0} = {60^0} + k{360^0}\\
3x - {15^0} = {120^0} + k{360^0}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
3x = {75^0} + k{360^0}\\
3x = {135^0} + k{360^0}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = {15^0} + k{120^0}\\
x = {45^0} + k{120^0}
\end{array} \right.\\
2)\cos 2x + 9\cos x - 10 = 0\\
\Leftrightarrow 2{\cos ^2}x - 1 + 9\cos x - 10 = 0\\
\Leftrightarrow 2{\cos ^2}x + 9\cos x - 11 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\cos x = 1\\
\cos x = - \frac{{11}}{2}\left( {VN} \right)
\end{array} \right. \Leftrightarrow x = k2\pi \\
3)\sin 2x - \sqrt 3 \cos 2x = 1\\
\Leftrightarrow \frac{1}{2}\sin 2x - \frac{{\sqrt 3 }}{2}\cos 2x = \frac{1}{2}\\
\Leftrightarrow \sin \left( {2x - \frac{\pi }{3}} \right) = \sin \frac{\pi }{6}\\
\Leftrightarrow \left[ \begin{array}{l}
2x - \frac{\pi }{3} = \frac{\pi }{6} + k2\pi \\
2x - \frac{\pi }{3} = \frac{{5\pi }}{6} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
2x = \frac{\pi }{2} + k2\pi \\
2x = \frac{{7\pi }}{6} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \frac{\pi }{4} + k\pi \\
x = \frac{{7\pi }}{{12}} + k\pi
\end{array} \right.\\
4)1 + \sin x - \cos 2x - \sin 3x = 0\\
\Leftrightarrow 1 + \sin x - \left( {1 - 2{{\sin }^2}x} \right) - \left( {3\sin x - 4{{\sin }^3}x} \right) = 0\\
\Leftrightarrow 1 + \sin x - 1 + 2{\sin ^2}x - 3\sin x + 4{\sin ^3}x = 0\\
\Leftrightarrow 4{\sin ^3}x + 2{\sin ^2}x - 2\sin x = 0\\
\Leftrightarrow \sin x\left( {2{{\sin }^2}x + \sin x - 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sin x = 0\\
\sin x = - 1\\
\sin x = \frac{1}{2}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = k\pi \\
x = - \frac{\pi }{2} + k\pi \\
x = \frac{\pi }{6} + k2\pi \\
x = \frac{{5\pi }}{6} + k2\pi
\end{array} \right.
\end{array}$
