已知sinx-cosx=1/2 sin³x－cos³x等于多少 已知sinx+cosx=1/2,则sin三次方x-cos三次...
\u5df2\u77e5sinx-cosx=1/2,\u6c42sin³x-cos³x\u7684\u503csinx-cosx=1/2(sinx-cosx)²=1/4(sinx)²+(cosx)²-2sinxcosx=1/4sinxcosx=3/8sin³x-cos³x=(sinx-cosx)(sin²x+sinxcosx+cos²x)=11/16
1\u3001\u82e5\u662f\u6c42sin³x-cos³x\u7684\u503c
\u89e3\uff1a
sin³x-cos³x=(sinx-cosx)(sin²x+cos²x+sinxcosx)
=(sinx-cosx)(1+sinxcosx)
\u56e0\u4e3a sinx+cosx=1/2\uff0c\u6240\u4ee5\uff08sinx+cosx)²=1/4\uff0c1+2sinxcosx=1/4
sinxcosx=-3/8
\u800c\u56e0\u4e3a(sinx-cosx)²=\uff08sinx+cosx)²-4sinxcosx=1/4-4*(-3/8)=7/4
\u2234sinx-cosx=\u00b1\u221a7/2
\u2234\u539f\u5f0f=\u00b1\u221a7/2*(1-3/8)=\u00b15\u221a7/16\u3010\u5373\u539f\u5f0f\u7b49\u4e8e\u6b63\u8d1f16\u5206\u4e4b5\u500d\u6839\u53f77\u3011
2\u3001\u82e5\u662f\u6c42sin³x+cos³x\u7684\u503c
\u89e3\uff1a
\u8bbesinx+cosx=m, \u5e73\u65b9
sin²+cos²x+2sinxcosx=1+2sinxcosx=m²
sinxcosx=(m²-1)/2
\u539f\u5f0f=(sinx+cosx)(sin²x-cosxsinx+cos²x)
=m[1-(m²-1)/2]
=(2m-m³+1)/2
\u5c06m=1/2\u4ee3\u5165\u4e0a\u5f0f\u5f97
\u539f\u5f0f=(2*1/2-1/8+1)/2
=15/16
简单分析一下，答案如图所示
cos3x=4cos³x-3cosx
(cosx-cos3x)÷sinx
=(cosx-(4cos³x-3cosx))÷sinx
=4cosx(1-cos²x)÷sinx
=4cosxsin²x÷sinx
=4cosxsinx
=2sin2x
所以(cosx-cos3x)÷sinx=2sin2x
希望能帮到你！
sinx-cosx=1/2
两边平方，
(sinx)的平方-2sinxcosx+(cosx)的平方=1/4
2sinxcosx=1-1/4=3/4
sinxcosx=3/8
(sinx)三次方-(cosx)三次方
=(sinx-cosx)(sinx 平方+sinxcosx+ cosx 平方)
=(1/2)(1+3/8)
=(1/2)(11/8 )
=11/16
sinx-cosx=1/2
(sinx-cosx)²=1/4
(sinx)²+(cosx)²-2sinxcosx=1/4
1-2sinxcosx=1/4
sinxcosx=3/8
sin³x-cos³x=(sinx-cosx)(sin²x+sinxcosx+cos²x)=11/16
供参考。请采纳。
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