[2(sinX)^2+2sinXcosX]/(1+tanX)=k (45°

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[2(sinX)^2+2sinXcosX]/(1+tanX)=k (45°
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[2(sinX)^2+2sinXcosX]/(1+tanX)=k (45°
[2(sinX)^2+2sinXcosX]/(1+tanX)=k (45°

[2(sinX)^2+2sinXcosX]/(1+tanX)=k (45°
(2sinx)^2+2sinxcosx=2sinx(sinx+cosx)
1+tanx=1+sinx/cosx=(sinx+cosx)/cosx
又45°

K=[2(sinx)^2+2sinxcosx]cosx/(sinx+cosx)=2sinxcosx
因为45°cosx.
(sinx-cosx)^2=(six)^2-2sinxcosx+(cos)^2=1-2sixcosx=1-k
所以sinx-cosx=(1-k)^1/2