Question

sinx*sin(60-x)*sin(60+x)=18

Answer 1

$sinx*sin(60-x)*sin(60+x)=frac{1}{8}\ sinx*(frac{cos(-2x)-cos(120)}{2})=frac{1}{8}\ sinx*(cos2x+0.5)=frac{1}{4}\ sinx(1.5-2sin^2x)=frac{1}{4}\ 6sinx-8sin^3x=1\ -8sin^3x+6sinx-1=0\ -2(3sinx-sin3x)+6sinx-1=0\ -2(3sinx-(4cos^2x-1)*sinx)+6sinx-1=0\ -2(3sinx-(4(1-sin^2x)-1)sinx)+6sinx-1=0\ -2(3sinx-(4-4sin^2x-1)sinx)+6sinx-1=0\ 2sin3x-1=0\ 2sin3x=1\ sin3x=frac{1}{2}\ x=frac{pi}{18}+frac{2pi*n}{3}\ x=frac{5pi}{18}+frac{2pi*n}{3}$