求证:1-2sinxcosxcos2x-sin2x=1-tanx1+tanx.-数学

题目简介

求证:1-2sinxcosxcos2x-sin2x=1-tanx1+tanx.-数学

题目详情

求证:
1-2sinxcosx
cos2x-sin2x
=
1-tanx
1+tanx
题型:解答题难度:中档来源:不详

答案

证明:∵左边=class="stub"1-2sinxcosx
cos2x-sin2x
=
cos2x+sin2x-2sinxcosx
cos2x-sin2x
=
(cosx-sinx)2
(cosx-sinx)×(cosx+sinx)
class="stub"cosx-sinx
cosx+sinx
=class="stub"1-tanx
1+tanx
=右边
class="stub"1-2sinxcosx
cos2x-sin2x
=class="stub"1-tanx
1+tanx
成立

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