问题 解答题
求证:
1-2sin2xcos2x
cos22x-sin22x
=
1-tan2x
1+tan2x
答案

证明:

左边=

sin22x+cos2x-2sin2xcos2x
cos22x-sin22x

=

(sin2x-cos2x)2
(cos2x+sin2x)(cos2x-sin2x)

=

cos2x-sin2x
sin2x+cos2x

=

cos2x
cos2x
-
sin2x
cos2x
cos2x
cos2x
-
sin2x
cox2x

=

1-tan2x
1+tan2x
=右边

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