求证:tan2x+1tan2x=2(3+cos4x)1-cos4x.-数学

题目简介

求证:tan2x+1tan2x=2(3+cos4x)1-cos4x.-数学

题目详情

求证:tan2x+
1
tan2x
=
2(3+cos4x)
1-cos4x
题型:解答题难度:中档来源:不详

答案

证明:左边=
sin2x
cos2x
+
cos2x
sin2x

=
sin4x+cos4x
sin2xcos2x

=
(sin2x+cos2x)2-2sin2xcos2x
class="stub"1
4
sin22x

=
8-4sin22x
1-cos4x
=
4+4cos22x
1-cos4x

=
4+2(1+cos4x)
1-cos4x
=
2(3+cos4x)
1-cos4x

=右边.
∴tan2x+class="stub"1
tan2x
=
2(3+cos4x)
1-cos4x

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