4cosa.cos (60-a) .cos (60 + a) = cos3a?
4cosa.cos (60-a) .cos (60 + a) = cos3a? Wir werden verwenden rarr2cosAcosB=cos(A+B)+cos(A-B)→2cosAcosB=cos(A+B)+cos(A−B) LHS=4cosxcos(60^@-x)cos(60^@+x)LHS=4cosxcos(60∘−x)cos(60∘+x) =2cosx*[2cos(60^@+x)cos(60^@-x)]=2cosx⋅[2cos(60∘+x)cos(60∘−x)] =2cosx*[cos(60^@+x+60^@-x)+cos(60^@+x-60^@+x)]=2cosx⋅[cos(60∘+x+60∘−x)+cos(60∘+x−60∘+x)] =2cosx[cos120^@+cos2x]=2cosx[cos120∘+cos2x] =2cosx[cos2x-1/2]=2cosx[cos2x−12] =cancel(2)cosx[(2cos2x-1)/cancel(2)] =2cos2x*cosx-cosx =cos(2x+x)+cos(2x-x)-cosx =cos3xcancel(+cosx)cancel(-cosx)=cos3x=RHS