Question

solve 2cos(2 theta)=1

Answer 1

Answer on Question #57363 – Math – Trigonometry

Question

Solve

$$2 \cos (2 \theta) = 1$$

Solution

$$2 \cos (2 \theta) = 1$$ $$\cos (2 \theta) = \frac {1}{2}$$ $$2 \theta = \arccos \left(\frac {1}{2}\right) + n \pi , n \in \mathbb {Z} \text{ (n is integer)},$$ $$2 \theta = \frac {\pi}{3} + n \pi , n \in \mathbb {Z} ,$$ $$\theta = \frac {\pi}{6} + \frac {n \pi}{2}, n \in \mathbb {Z}.$$

Answer: $\theta = \frac{\pi}{6} +\frac{n\pi}{2},n\in \mathbb{Z}.$

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