Question

If $x_1$ and $x_2$ are the two solutions of the equation $2 \cos x \sin 3 x=\sin 4 x+1$ lying in the interval $[0,2 \pi]$, then the value of $\left|x_1-x_2\right|$ is

• A. $\frac{\pi}{4}$
• B. $\frac{\pi}{2}$
• C. $\pi$
• D. $2 \pi$

Answer 1

Answer: (C)

$\sin 4 x+\sin 2 x=\sin 4 x+1$
$\therefore \sin 2 x=1 $
$\Rightarrow 2 x=\frac{\pi}{2} \text { or } \frac{5 \pi}{2} $
$\therefore x=\frac{\pi}{4}, \frac{5 \pi}{4} $
$\therefore\left|x_1-x_2\right|=\pi$