Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
a)\,\,\tan \left( {4x - \frac{\pi }{3}} \right) = \sqrt 3 \\
\Leftrightarrow \tan \left( {4x - \frac{\pi }{3}} \right) = \tan \frac{\pi }{3}\\
\Leftrightarrow 4x - \frac{\pi }{3} = \frac{\pi }{3} + k\pi \\
\Leftrightarrow 4x = \frac{{2\pi }}{3} + k\pi \\
\Leftrightarrow x = \frac{\pi }{6} + \frac{{k\pi }}{4}\\
b)\,\,\sin \left( {2x - 40^\circ } \right) = \frac{{\sqrt 3 }}{2}\\
\Leftrightarrow \sin \left( {2x - 40^\circ } \right) = \sin 60^\circ \\
\Leftrightarrow \left[ \begin{array}{l}
2x - 40^\circ = 60^\circ + k.360^\circ \\
2x - 40^\circ = 120^\circ + k.360^\circ
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
2x = 100^\circ + k.360^\circ \\
2x = 160^\circ + k.360^\circ
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 50^\circ + k.360^\circ \\
x = 80^\circ + k.360^\circ
\end{array} \right.
\end{array}\)
