Question

16sin^5(x)-20sin^3(x)+5sin(x)

Answer 1

$16sin^5x-20sin^3x+5sinx=0$
$5sinx-20*( frac{3sinx-sin3x}{4} )+16sin^5x=0$

$5sinx-20*( frac{3sinx}{4} - frac{sin3x}{4} )+16sin^5x=0$

$5sinx-20*( frac{3sinx}{4} - frac{sin3x}{4} )+16*( frac{10sinx-5sin3x+sin5x}{16} )=0$

$5sinx-20*( frac{3sinx}{4} - frac{sin3x}{4})+16*(frac{5sinx}{8}-frac{5sin3x}{16}+frac{sin5x}{16})=0$

$5sinx+(5sin3x-15sinx)+16*(frac{5sinx}{8}-frac{5sin3x}{16}+frac{sin5x}{16})=0$

$5sinx-15sinx+5sin3x+(10sinx-5sin3x+sin5x)=0$

$sin5x=0$

$5x= pi n$; n∈Z
$x= frac{ pi n}{5}$; n∈Z