\cos(x)\cos(2x)\cos(4x)=\frac{(\sin(x)\cos(x))\cos(2x)\cos(4x)}{\sin(x)}=\frac{(\sin(2x)\cos(2x))\cos(4x)}{2\sin(x)}=\frac{\sin(4x)\cos(4x)}{4\sin(x)}=\frac{\sin(8x)}{8\sin(x)}