Find the general solution of equation \(\cos 5\theta = \frac{1}{2}\).
Q.5 Find the general solution of equation \(\cos 5\theta = \frac{1}{2}\).
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Answer: \(\theta = \frac{2n\pi}{5} \pm \frac{\pi}{15},\ n \in Z\)
\(\cos 5\theta = \frac{1}{2} = \cos\frac{\pi}{3}\).
The general solution of \(\cos\theta = \cos\alpha\) is \(\theta = 2n\pi \pm \alpha\). So \(5\theta = 2n\pi \pm \frac{\pi}{3}\), i.e. \(\theta = \frac{2n\pi}{5} \pm \frac{\pi}{15}\), where \(n \in Z\).
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· 28 Oct 2026
AI-verified · Oct 2026
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