8 sin 8 α = 8 sin α ∗ cos α ∗ cos 2 α ∗ cos 4 α {\displaystyle \ 8\sin {8\alpha }=8\sin \alpha *\cos \alpha *\cos {2\alpha }*\cos {4\alpha }}
פתירת אגף שמאל:
8 sin 8 α sin 2 α = 2 sin α cos α ↓ 2 sin 4 α ∗ cos 4 α sin 2 α = 2 sin α ∗ cos α ↓ 2 ∗ 2 sin 2 α ∗ cos 2 α ∗ cos 4 α 4 ∗ 2 ∗ sin α ∗ cos α ∗ cos 2 α ∗ cos 4 α {\displaystyle {\begin{aligned}&\color {green}8\sin {8\alpha }\\&\color {blue}\sin 2\alpha =2\sin \alpha \cos \alpha \\&\downarrow \\&2{\color {green}\sin {4\alpha }}*\cos {4\alpha }\\&\color {blue}\sin 2\alpha =2\sin \alpha *\cos \alpha \\&\downarrow \\&2*2{\color {green}\sin {2\alpha }}*\cos {2\alpha }*\cos {4\alpha }\\&4*2*\sin \alpha *\cos \alpha *\cos {2\alpha }*\cos {4\alpha }\\\end{aligned}}}
