Giải phương trình: cos ( x + 2 pi/ 3 ) = √ 2 /2 .

22/39

Giải phương trình: \(\cos \left( {x + \frac{{2\pi }}{3}} \right) = \frac{{\sqrt 2 }}{2}\).

\(\left[ \begin{array}{l}x = - \frac{{5\pi }}{{12}} + k2\pi \\x = - \frac{{11\pi }}{{12}} + k2\pi \end{array} \right.\left( {k \in \mathbb{Z}} \right)\).

\(\left[ \begin{array}{l}x = - \frac{{5\pi }}{{12}} + k2\pi \\x = \frac{{11\pi }}{{12}} + k2\pi \end{array} \right.\left( {k \in \mathbb{Z}} \right)\).

\(\left[ \begin{array}{l}x = - \frac{{5\pi }}{{12}} + k2\pi \\x = \frac{{7\pi }}{{12}} + k2\pi \end{array} \right.\left( {k \in \mathbb{Z}} \right)\).

\(\left[ \begin{array}{l}x = \frac{{5\pi }}{{12}} + k2\pi \\x = \frac{{7\pi }}{{12}} + k2\pi \end{array} \right.\left( {k \in \mathbb{Z}} \right)\).

Giải thích

Chọn A

Ta có \(\cos \left( {x + \frac{{2\pi }}{3}} \right) = \frac{{\sqrt 2 }}{2}\)\( \Leftrightarrow \left[ \begin{array}{l}x + \frac{{2\pi }}{3} = \frac{\pi }{4} + k2\pi \\x + \frac{{2\pi }}{3} = - \frac{\pi }{4} + k2\pi \end{array} \right.\left( {k \in \mathbb{Z}} \right) \Leftrightarrow \left[ \begin{array}{l}x = - \frac{{5\pi }}{{12}} + k2\pi \\x = - \frac{{11\pi }}{{12}} + k2\pi \end{array} \right.\left( {k \in \mathbb{Z}} \right)\).