# Math Help - find x

1. ## find x

x is acute angle and

$\sin 5x \sin 4x=\sin 3x \sin 8x$

find x

2. Originally Posted by perash
x is acute angle and

$\sin 5x \sin 4x=\sin 3x \sin 8x$

find x
Well, it's clear how some of the solutions can be got:

$\sin 5x \sin 4x=\sin 3x \sin 8x \, \Rightarrow \, \sin 5x \sin 4x= 2 \sin 3x \sin 4x \cos 4x$.

Therefore either:

$\sin 4x = 0 \,$ or $\, \sin 5x = 2 \sin 3x \cos 4x$.

The first of these equations gives $x = 0, \, \frac{\pi}{4}$ as (obvious) solutions. So there are only three other solutions to get .....