Question

If $5x = 2n\pi \pm (\pi - x)$ and $\Rightarrow$is an acute angle, then $x = \frac{(2n + 1)\pi}{6}$.

• A. $\frac{(2n - 1)\pi}{4}$
• B. $\therefore$
• C. 0
• D. None of these

Answer 1

Answer: (A)

$\frac{(2n - 1)\pi}{4}$

Answer 2

$k \in Z2\cos\theta = 0$ $\theta = 2n\pi \pm \frac{\pi}{2}$

$\tan(3x - 2x) = \tan x = 1x = n\pi + \frac{\pi}{4}$ or $\tan\theta + \tan 2\theta + \sqrt{3}\tan\theta\tan 2\theta = \sqrt{3}$.

Since $\tan\theta + \tan 2\theta = \sqrt{3}(1 - \tan\theta\tan 2\theta)$ is acute

⇒ $\sqrt{3}$ ⇒ $\tan 3\theta = \tan(\pi/3)$.