y=4sinx+4sin(2π/3-x)+2根号3 化简y=4sinx+4sin(2π/3-x)+2

网友回答

y=4sinx+4sin(2π/3-x)+2根号3
=4sinx+4sin(π - π/3-x)+2根号3
=4sinx+4sin(π/3+x)+2根号3
=4*[sinx+ sin(π/3)cosx + sin(π/3)sinx] +2根号3
=4*[sinx+ (根号3/2)*cosx + (1/2)*sinx] +2根号3
=4*[(3/2)*sinx+(根号3/2)*cosx ] +2根号3
=4根号3*[sinx*(根号3/2)+cosx*(1/2) ] +2根号3
=4根号3*[sinx*cos(π/6)+cosx*sin(π/6) ] +2根号3
=4根号3*sin(x + π/6) +2根号3