Nghiệm của phương trình cos ( 3x + pi/ 4 ) = − √ 2/2 là

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Nghiệm của phương trình \(\cos \left( {3x + \frac{\pi }{4}} \right) = - \frac{{\sqrt 2 }}{2}\) là

\(\left[ \begin{array}{l}x = \frac{\pi }{6} + k\frac{{2\pi }}{3}\\x = - \frac{\pi }{3} + k\frac{{2\pi }}{3}\end{array} \right.\).

\(\left[ \begin{array}{l}x = \frac{\pi }{4} + k\frac{{2\pi }}{3}\\x = - \frac{\pi }{4} + k\frac{{2\pi }}{3}\end{array} \right.\).

\(\left[ \begin{array}{l}x = \frac{\pi }{6} + k\frac{\pi }{6}\\x = - \frac{\pi }{3} + k\frac{\pi }{6}\end{array} \right.\).

\(\left[ \begin{array}{l}x = \frac{\pi }{6} + k\frac{{2\pi }}{3}\\x = - \frac{{4\pi }}{3} + k\frac{{2\pi }}{3}\end{array} \right.\).

Giải thích

Chọn A

\(\cos \left( {3x + \frac{\pi }{4}} \right) = - \frac{{\sqrt 2 }}{2}\)

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

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

\( \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{6} + k\frac{{2\pi }}{3}\\3x = - \frac{\pi }{3} + k\frac{{2\pi }}{3}\end{array} \right.\left( {k \in \mathbb{Z}} \right)\).