+5 sin(4x)cos(8x)-cos(4x)sin(8x)=-.4 for smallest positive solution
+14903 sin(4x)cos(8x)-cos(4x)sin(8x)=-.4 for smallest positive solution
Hello carlos!
\(sin(4x)cos(8x)-cos(4x)sin(8x)=-0.4 \)
\(sin(\alpha-\beta)=sin(\alpha)cos(\beta)-cos(\alpha)sin(\beta)\ \color{black}\small{(Bartsch\ Leipzig\ 1980)}\)
\(\alpha=4x\\ \beta =8x\)
\(sin(4x-8x)=sin(4x)cos(8x)-cos(4x)sin(8x)=-0.4\)
\(sin(-4x)=-0.4\)
\(-4x=arcsin(-0.4)\\ x= \frac{arcsin(-0.4)}{-4}\)
\(x=0.102879211517\)
!
