Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
c,\\
\sin \left( {5x - \dfrac{{3\pi }}{4}} \right) + \cos \left( {2x + \dfrac{\pi }{3}} \right) = 0\\
\Leftrightarrow \cos \left( {2x + \dfrac{\pi }{3}} \right) = - \sin \left( {5x - \dfrac{{3\pi }}{4}} \right)\\
\Leftrightarrow \cos \left( {2x + \dfrac{\pi }{3}} \right) = \sin \left( {\dfrac{{3\pi }}{4} - 5x} \right)\\
\Leftrightarrow \cos \left( {2x + \dfrac{\pi }{3}} \right) = \cos \left( {\dfrac{\pi }{2} - \left( {\dfrac{{3\pi }}{4} - 5x} \right)} \right)\\
\Leftrightarrow \cos \left( {2x + \dfrac{\pi }{3}} \right) = \cos \left( {5x - \dfrac{\pi }{4}} \right)\\
\Leftrightarrow \left[ \begin{array}{l}
2x + \dfrac{\pi }{3} = 5x - \dfrac{\pi }{4} + k2\pi \\
2x + \dfrac{\pi }{3} = \dfrac{\pi }{4} - 5x + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{{7\pi }}{{36}} + \dfrac{{k2\pi }}{3}\\
x = \dfrac{{ - \pi }}{{84}} + \dfrac{{k2\pi }}{7}
\end{array} \right.\\
d,\\
\tan \left( {x - 20^\circ } \right) + \cot \left( { - 2x + 15^\circ } \right) = 0\\
\Leftrightarrow \tan \left( {x - 20^\circ } \right) = - \cot \left( { - 2x + 15^\circ } \right)\\
\Leftrightarrow \tan \left( {x - 20^\circ } \right) = \cot \left( {2x - 15^\circ } \right)\\
\Leftrightarrow \tan \left( {x - 20^\circ } \right) = \tan \left[ {90^\circ - \left( {2x - 15^\circ } \right)} \right]\\
\Leftrightarrow \tan \left( {x - 20^\circ } \right) = \tan \left( {105^\circ - 2x} \right)\\
\Leftrightarrow x - 20^\circ = 105^\circ - 2x + k.180^\circ \\
\Leftrightarrow x = \dfrac{{125^\circ }}{3} + k.60^\circ
\end{array}\)
