Giải phương trình cos(2x - pi/3) = - (CĂN 3)/2

9/21

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

\(\left[ {\begin{array}{*{20}{c}}{x = \frac{{7\pi }}{{12}} + k2\pi }\\{x = - \frac{\pi }{4} + k2\pi }\end{array}} \right.\,\,\left( {k \in \mathbb{Z}} \right)\).

\(\left[ {\begin{array}{*{20}{c}}{x = \frac{{7\pi }}{{12}} + k\pi }\\{x = - \frac{\pi }{4} + k\pi }\end{array}} \right.\,\left( {k \in \mathbb{Z}} \right)\).

\(x = \pm \frac{{5\pi }}{6} + k\pi \,\left( {k \in \mathbb{Z}} \right)\).

\(x = \pm \frac{{5\pi }}{6} + k2\pi \,\left( {k \in \mathbb{Z}} \right)\).

Giải thích

Ta có \( - \frac{{\sqrt 3 }}{2} = \cos \frac{{5\pi }}{6}\). Khi đó phương trình tương đương với:

\(\left[ {\begin{array}{*{20}{c}}{2x - \frac{\pi }{3} = \frac{{5\pi }}{6} + k2\pi }\\{2x - \frac{\pi }{3} = - \frac{{5\pi }}{6} + k2\pi }\end{array}} \right. \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{2x = \frac{{7\pi }}{6} + k2\pi }\\{2x = - \frac{\pi }{2} + k2\pi }\end{array}} \right. \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{x = \frac{{7\pi }}{{12}} + k\pi }\\{x = - \frac{\pi }{4} + k\pi }\end{array}\quad \left( {k \in \mathbb{Z}} \right)} \right.\).

Chọn B.