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

Trigonometric Functions

Solution:

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