Come dimostrate cos 3 theta = 4 cos ^ 3 theta – 3 cos theta ?
Come dimostrate cos 3 theta = 4 cos ^ 3 theta – 3 cos theta ? Risposta: La prova è riportata di seguito. Spiegazione: cos3theta=cos(2theta+theta) =cos2thetacostheta-sin2thetasintheta =(cos^2theta-sin^2theta)costheta-2sinthetacosthetasintheta =cos^3theta-sin^2costheta-2sin^2thetacostheta =costheta(cos^2theta-sin^2theta-2sin^2theta) =costheta(cos^2theta-3sin^2theta) =cos^3theta-3sin^2thetacostheta =cos^3theta-3(1-cos^2theta)costheta =cos^3theta-3costheta+3cos^3theta =4cos^3theta-3costheta