Question

If $\tan\theta = 0 \Rightarrow \theta = m\pi$, the general value of $\theta = \pm \sqrt{3} = \tan( \pm \frac{\pi}{3})\ \Rightarrow \theta = n\pi \pm \frac{\pi}{3}$ is.

• A. $\theta = m\pi,n\pi \pm \frac{\pi}{3}$
• B. $\cos 2\theta = \cos\left( \frac{\pi}{2} - \alpha \right) \Rightarrow 2\theta = 2n\pi \pm \left( \frac{\pi}{2} - \alpha \right)$
• C. $\Rightarrow$
• D. $\theta = n\pi \pm \left( \frac{\pi}{4} - \frac{\alpha}{2} \right)$

Answer 1

Answer: (C)

$\Rightarrow$

Answer 2

$\Rightarrow$ ⇒ $\cos\theta = \frac{2(\sqrt{3} + 1) \pm \sqrt{4(\sqrt{3} + 1)^{2} - 16\sqrt{3}}}{8}$

$\sin \theta = 0$ $\cot\theta + \cot\left( \frac{\pi}{4} + \theta \right) = 2 \Rightarrow \frac{\cos\theta}{\sin\theta} + \frac{\cos\{(\pi/4) + \theta\}}{\sin\{(\pi/4) + \theta\}} = 2$ $\Rightarrow$or $\sin\left( \frac{\pi}{4} + 2\theta \right) = 2\sin\theta\sin\left( \frac{\pi}{4} + \theta \right)$.