Question

If $\theta = \frac{\pi}{4}$, then $\cos 3\theta = \frac{1}{2}$

• A. $\Rightarrow$
• B. $3\theta = \frac{\pi}{3}$
• C. $\Rightarrow$
• D. $\theta = \frac{\pi}{9}$

Answer 1

Answer: (D)

$\theta = \frac{\pi}{9}$

Answer 2

$\Rightarrow$

$\Rightarrow$ $\cot\theta = \sin 2\theta,\text{ }(\theta \neq n\pi) \Rightarrow 2\sin^{2}\theta\cos\theta = \cos\theta$

$\Rightarrow$ $\cos\theta = 0$

$\sin^{2}\theta = \frac{1}{2} = \sin^{2}\left( \frac{\pi}{4} \right) \Rightarrow$

$\theta = (2n + 1)\frac{\pi}{2}\theta = n\pi \pm \frac{\pi}{4}$.