问题 选择题
1-2sin(π+2)cos(π+2)
等于(  )
A.sin2-cos2B.cos2-sin2C.±(sin2-cos2)D.sin2+cos2
答案

π
2
<2<π,

∴sin2>0,cos2<0,即sin2-cos2>0,

1-2sin(π+2)cos(π+2)

=

1-2sin2cos2

=

sin22+cos22-2sin2cos2

=

(sin2-cos2)2

=|sin2-cos2|,(又2是钝角)

=sin2-cos2.

故选A

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