Question

$\cos 4x\cos 8x-\cos 5x\cos 9x=0$ if

• A. $\cos 12x=\cos 14x$
• B. $\sin 13x=0$
• C. $\sin x=0$
• D. all of these

Answer 1

Answer: (D)

$\cos 4x\cos 8x-\cos 5x\cos 9x=0$
$\Rightarrow 2\cos 4x\cos 8x=2\cos 5x\cos 9x$
$\Rightarrow \cos 12x+\cos 4x=\cos 14x+\cos 4x$
$\Rightarrow 14x=2n\pi \pm (12x)$
$\Rightarrow 2x=2n\pi$ or $26x=2n\pi$
$\Rightarrow x=n\pi$ or $\frac{n\pi }{13}$
$\therefore \sin x=0$ or $\sin 13x=0$