Giải các phương trình sau a) sin ( 3x − 7pi/ 12 ) = sin ( − x +pi/4 ) ;

a) \(\sin \left( {3x - \frac{{7\pi }}{{12}}} \right) = \sin \left( { - x + \frac{\pi }{4}} \right)\)\( \Leftrightarrow \left[ \begin{array}{l}3x - \frac{{7\pi }}{{12}} = - x + \frac{\pi }{4} + k2\pi \\3x - \frac{{7\pi }}{{12}} = \pi - \left( { - x + \frac{\pi }{4}} \right) + k2\pi \end{array} \right.\)\( \Leftrightarrow \left[ \begin{array}{l}x = \frac{{5\pi }}{{24}} + k\frac{\pi }{2}\\x = \frac{{2\pi }}{3} + k\pi \end{array} \right.,k \in \mathbb{Z}\).

b) \(\sin 3x - \cos \left( {\frac{{3\pi }}{4} - x} \right) = 0\)\( \Leftrightarrow \cos \left( {\frac{\pi }{2} - 3x} \right) = \cos \left( {\frac{{3\pi }}{4} - x} \right)\)\( \Leftrightarrow \left[ \begin{array}{l}\frac{\pi }{2} - 3x = \frac{{3\pi }}{4} - x + k2\pi \\\frac{\pi }{2} - 3x = - \frac{{3\pi }}{4} + x + k2\pi \end{array} \right.\)

\( \Leftrightarrow \left[ \begin{array}{l}x = - \frac{\pi }{8} + k\pi \\x = \frac{{5\pi }}{{16}} + k\frac{\pi }{2}\end{array} \right.,k \in \mathbb{Z}\).