1-cosx=sinx²吗
sin²x(1-cosx)\u7684\u5bfc\u6570y=sin²x(1-cosx)
=(1-cos²x)(1-cosx)
=1-cosx-cos²x+cos³x
y'=0+sinx-2cosx *(cosx)'+3cos²x * (cosx)'
=sinx+2sinxcosx-3sinxcos²x
\u6216\u8005\uff1a
y'=(sin²x)'(1-cox)+(sin²x)(1-cox)'
=2sinxcosx(1-cosx)+sin²x(0+sinx)
=2sinxcosx-2sinxcos²x+sin³x
\u4ee5\u4e0b\u53ef\u7701\u7565\uff0c\u53ea\u662f\u4e3a\u53d8\u5f62\u5230\u4e0e\u524d\u8005\u76f8\u540c\u5f62\u5f0f
=2sinxcosx-sinx(2cos²x-sin²x)
=2sinxcosx-sinx(3cos²x-cos²x-sin²x)
=2sinxcosx-sinx(3cos²-1)
=2sinxcosx+sinx-3sinxcos²x
sinx=1+cosx
sin²x+cos²x=1
\u6240\u4ee5(1+cosx)²+cos²x=1\uff0c\u89e3\u5f97cosx=0\uff0csinx=1\u6216cosx=-1\uff0csinx=0
\u6240\u4ee5sinx+cosx=1\u6216-1
正确的公式是sin²x+cos²x=1
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