1-2sin(π+2)cos(π+2)等于()A.sin2-cos2B.cos2-sin2C.±(sin2-cos2)D.sin2+cos2-数学

题目简介

1-2sin(π+2)cos(π+2)等于()A.sin2-cos2B.cos2-sin2C.±(sin2-cos2)D.sin2+cos2-数学

题目详情

1-2sin(π+2)cos(π+2)
等于(  )
A.sin2-cos2B.cos2-sin2C.±(sin2-cos2)D.sin2+cos2
题型:单选题难度:偏易来源:不详

答案

class="stub"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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