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Question
If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are
Options
- \[x = \frac{\pi}{3}, \frac{4\pi}{3}\]
- \[x = \frac{2\pi}{3}, \frac{4\pi}{3}\]
- \[x = \frac{2\pi}{3}, \frac{7\pi}{6}\]
- \[\theta = \frac{2\pi}{3}, \frac{5\pi}{3}\]
Solution
Given equation:
\[\cos x = - \frac{1}{2}\]
\[ \Rightarrow \cos x = \cos \frac{2\pi}{3}\]
\[ \Rightarrow x = \frac{2\pi}{3}\]
Or,
\[\cos x = \cos \frac{4\pi}{3}\]
\[ \Rightarrow x = \frac{4\pi}{3}\]
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