Question

The general solution of $\tan\left( 3\theta - \frac{\pi}{4} \right) = \tan\frac{\pi}{3}$ is.

• A. $3\theta - (\pi/4) = n\pi + (\pi/3)$
• B. $3\theta = n\pi + \frac{7\pi}{12}$
• C. $\theta = \frac{n\pi}{3} + \frac{7\pi}{36}$
• D. $2 - 2\sin^{2}x + 3\sin x - 3 = 0$

Answer 1

Answer: (B)

$3\theta = n\pi + \frac{7\pi}{12}$

Answer 2

The given equation can be written as

$\sin 4\theta(2\cos 2\theta + 1) = 0 \Rightarrow 2\cos 2\theta = - 1$ $\Rightarrow$

$\cos 2\theta = - \frac{1}{2}$ $\Rightarrow$ $2\theta = 2n\pi \pm \frac{2\pi}{3} \Rightarrow \theta = n\pi \pm \frac{\pi}{3}$ $\sin 4\theta = 0 \Rightarrow 4\theta = n\pi \Rightarrow \theta = \frac{n\pi}{4}\theta = \frac{n\pi}{4}$.