cos 8 α cos3 α =(1/2)cos(8 α +3 α )+(1/2)cos(8 α -3 α )=(1/2)cos11 α +(1/2)cos5 α
cos 7 α cos4 α -cos 8 α cos3 α=(1/2)cos11 α +(1/2)cos3 α -(1/2)cos11 α - (1/2)cos5 α =(1/2)cos3 α - (1/2)cos5 α =
=(1/2)*(-2 sin(3 α +5 α )/2)*sin((3 α -5 α)/2=
=sin4 α *sin α
если
cos α =[b]a[/b], тогда
sin α = ± sqrt(1-cos^2 α )= ± sqrt(1-[b]a[/b]^2)
sin4 α =2sin2 α *cos2 α =2sin α *cos α (1+2cos^2 α )= ± 2sqrt(1-[b]a[/b]^2) * [b]a[/b]* (1+2[b]a[/b]^2)
sin4 α *sin α =± 2sqrt(1-[b]a[/b]^2) * [b]a[/b]* (1+2[b]a[/b]^2) * (± sqrt(1-[b]a[/b]^2))=
=[red][b]2*(1-a^2)*a*(1+2a^2)[/b][/red]