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(sinx)^3+(cosx)^3 最大值是多少
(sinx)^3+(cosx)^3 最大值是多少
数学人气:642 ℃时间:2020-09-23 07:52:21
优质解答
(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...
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