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Question
Solve the following equation:
Solution
\[ \Rightarrow 4 \cos^2 x + 8 \cos x - 5 = 0\]
\[ \Rightarrow 4 \cos^2 x + 10 \cos x - 2 \cos x - 5 = 0\]
\[ \Rightarrow 2 \cos x (2 \cos x + 5 ) - 1 (2 \cos x + 5) = 0\]
\[ \Rightarrow (2 \cos x - 1) (2 \cos x + 5) = 0\]
\[\therefore 2 \cos x - 1 = 0 \]
\[ \Rightarrow \cos x = \frac{1}{2} \]
\[ \Rightarrow \cos x = \cos \frac{\pi}{3} \]
\[ \Rightarrow x = 2n\pi \pm \frac{\pi}{3}, n \in Z\]
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