(sinx)^3+(cosx)^3=(sinx+cosx)(sin^2x-sinxcosx+cos^2x).=√2sin(x+45°)[1-(1/2)sin2x].当 sin2x=0,2x=0,x=0 时,(sin^3x+cos^3x)max=√2sin(x+45°)=√2sin45°=√2*√2/2=1.或当 sin2x=0,2x=180°,x=90° 时,原式...