x is acute angle and
$\displaystyle \sin 5x \sin 4x=\sin 3x \sin 8x$
find x
Well, it's clear how some of the solutions can be got:
$\displaystyle \sin 5x \sin 4x=\sin 3x \sin 8x \, \Rightarrow \, \sin 5x \sin 4x= 2 \sin 3x \sin 4x \cos 4x$.
Therefore either:
$\displaystyle \sin 4x = 0 \,$ or $\displaystyle \, \sin 5x = 2 \sin 3x \cos 4x$.
The first of these equations gives $\displaystyle x = 0, \, \frac{\pi}{4}$ as (obvious) solutions. So there are only three other solutions to get .....