求证：1−2sin2xcos2xcos22x−sin22x＝1−tan2x1+tan2x．
问题描述：
求证：
＝1−2sin2xcos2x
cos22x−sin22x
． 1−tan2x 1+tan2x
答
证明：左边=
cos22x+sin22x−2sin2xcos2x cos22x−sin22x
=
(sin2x−cos2x)2 (cos2x+sin2x)(cos2x−sin2x)
=
cos2x−sin2x sin2x+cos2x
=
=右边1−tan2x 1+tan2x