Question

If $\tan 5\theta = \tan\left( \frac{\pi}{2} - 2\theta \right)$, then the general value of $\Rightarrow$ is.

• A. $5\theta = n\pi + \frac{\pi}{2} - 2\theta$
• B. $\Rightarrow$
• C. $7\theta = n\pi + \frac{\pi}{2}$
• D. $\Rightarrow$

Answer 1

Answer: (D)

$\Rightarrow$

Answer 2

$\sin\theta + \cos\theta = \sqrt{2}\cos\alpha \Rightarrow \cos\left( \theta - \frac{\pi}{4} \right) = \cos\alpha$

$\Rightarrow \theta - \frac{\pi}{4} = 2n\pi \pm \alpha \Rightarrow \theta = 2n\pi + \frac{\pi}{4} \pm \alpha$

$\Rightarrow$ $\tan 6\theta = \frac{\tan\theta + \tan 2\theta + \tan 3\theta - \tan\theta\tan 2\theta\tan 3\theta}{1 - \sum\tan\theta\tan 2\theta}$

$\Rightarrow 6\theta = n\pi \Rightarrow \theta = n\pi/6$.