化简(sinx+cosx-1)(sinx-cosx+1)sin2x.-数学

题目简介

化简(sinx+cosx-1)(sinx-cosx+1)sin2x.-数学

题目详情

化简
(sinx+cosx-1)(sinx-cosx+1)
sin2x
题型:解答题难度:中档来源:不详

答案

原式=
(sinx+1-2sin2class="stub"x
2
-1)(sinx-1+2sin2class="stub"x
2
+1)
sin2x

=
(2sinclass="stub"x
2
cosclass="stub"x
2
-2sin2class="stub"x
2
)(2sinclass="stub"x
2
cosclass="stub"x
2
+2sin2class="stub"x
2
)
4sinclass="stub"x
2
cosclass="stub"x
2
cosx

=
(cosclass="stub"x
2
-sinclass="stub"x
2
)(cosclass="stub"x
2
+sinclass="stub"x
2
)•sinclass="stub"x
2
cosclass="stub"x
2
cosx

=
(cos2class="stub"x
2
-sin2class="stub"x
2
)sinclass="stub"x
2
cosclass="stub"x
2
•cosx
=
cosx•sinclass="stub"x
2
cosclass="stub"x
2
•cosx
=tanclass="stub"x
2

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