SIN (90-X)=2SIN (X)

2sin(x\uff0d45\u5ea6\uff09sin(x\uff0b45\u5ea6\uff09\u600e\u4e48\u53d8\u6210sin(2x\uff0d90\u5ea6\uff09\u89e3\u91ca\u4ed4\u7ec6\u70b9

\u5c06\u91cc\u9762\u7684\u5206\u522b\u76f8\u4e58=sin^2-cos^2x=1-2cos^2x=-(2cos^2x-1)=-cos2x=sin(2x-90\u00b0

2sin(x+\u03c0/4)sin(x-\u03c0/4)
=2sin(x+\u03c0/4)sin[-\u03c0/2+(\u03c0/4+x)]
=-2sin(x+\u03c0/4)cos(\u03c0/4+x)
=-sin(2x+\u03c0/2)
=-cos2x

2sin(x+\u03c0/4)sin(x-\u03c0/4)
=2(sinxcos\u03c0/4+cosxsin\u03c0/4)(sinxcos\u03c0/4-cosxsin\u03c0/4)
=2*(\u221a2/2)²(sinx+cosx)(sinx-cosx)
=sin²x-cos²x
=-(cos²x-sin²x)
=-cos2x

可以拆开
sin(90-x)
=sin90cosx-cos90sinx
=cosx

=2sinx
那么cosx=2sinx
了求什么

sin(90-x)=cosx=2sinx
tanx=1/2
x=arctan(1/2)=26.57°

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