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Question
Solve the following equation:
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Solution
\[\cos x + \cos 2x + \cos 3x = 0\]
Now,
\[(\cos x + \cos3x) + \cos2x = 0\]
\[ \Rightarrow 2 \cos \left( \frac{4x}{2} \right) \cos \left( \frac{2x}{2} \right) + \cos2x = 0\]
\[ \Rightarrow 2 \cos2x \cos x + \cos2x = 0\]
\[ \Rightarrow \cos2x ( 2 \cos x + 1) = 0\]
\[x = 2m\pi \pm \frac{2\pi}{3}, m \in Z\]
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