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#