Giải các phương trình sau a) sin ( 3 x − 3 π /4 ) = sin ( π /6 − x ) ;

a) \(\sin \left( {3x - \frac{{3\pi }}{4}} \right) = \sin \left( {\frac{\pi }{6} - x} \right) \Rightarrow \left[ {\begin{array}{*{20}{c}}{3x - \frac{{3\pi }}{4} = \frac{\pi }{6} - x + k2\pi }\\{3x - \frac{{3\pi }}{4} = \pi - \left( {\frac{\pi }{6} - x} \right) + k2\pi }\end{array}} \right. \Rightarrow \left[ {\begin{array}{*{20}{c}}{x = \frac{{11\pi }}{{48}} + \frac{{k\pi }}{2}}\\{x = \frac{{19\pi }}{{24}} + k\pi }\end{array}} \right.,k \in \mathbb{Z}\).

b) \(\cos \left( {2x + 25^\circ } \right) = - \frac{{\sqrt 2 }}{2} \Rightarrow \cos \left( {2x + 25^\circ } \right) = \cos 135^\circ \)

\( \Rightarrow \left[ {\begin{array}{*{20}{c}}{2x + 25^\circ = 135^\circ + k360^\circ }\\{2x + 25^\circ = - 135^\circ + k360^\circ }\end{array}} \right. \Rightarrow \left[ {\begin{array}{*{20}{c}}{x = 55^\circ + k180^\circ }\\{x = - 80^\circ + k180^\circ }\end{array}} \right.,k \in \mathbb{Z}\).