Question

The values of $\because$ satisfying $- \pi \leq x \leq \pi$ and $\therefore$ are.

• A. $x = \pm \frac{\pi}{4}, \pm \frac{\pi}{2}, \pm \frac{3\pi}{4}$
• B. $\sin 7\theta + \sin\theta - \sin 4\theta = 0$
• C. $\Rightarrow$
• D. $2\sin 4\theta\cos 3\theta - \sin 4\theta = 0$

Answer 1

Answer: (A)

$x = \pm \frac{\pi}{4}, \pm \frac{\pi}{2}, \pm \frac{3\pi}{4}$

Answer 2

$\Rightarrow$

$\Rightarrow$ $\cos\theta = - \frac{1}{\sqrt{2}} \Rightarrow \theta = \frac{3\pi}{4},\frac{5\pi}{4}$

$\tan\theta = 1 \Rightarrow \theta = \frac{\pi}{4},\frac{5\pi}{4}$ $\therefore$

Now sin$2n\pi + \frac{5\pi}{4}$ $(2n + 1)\pi + \frac{\pi}{4}$ $\sin(A + B) = 1$ $\cos(A - B) = \frac{\sqrt{3}}{2}$ $\Rightarrow$.

And $A + B = \frac{\pi}{2}$ $A - B = \frac{\pi}{6}$ $\Rightarrow$ $A = \frac{\pi}{3},B = \frac{\pi}{6}$ $2 - 2\cos^{2}\theta + \sqrt{3}\cos\theta + 1 = 0$.