求证:tan(x+y)+tan(x-y)=sin2x/cos2x−sin2y.
问题描述:
求证:tan(x+y)+tan(x-y)=
. sin2x
cos2x−sin2y
答
证明:左=
+sin(x+y) cos(x+y)
sin(x−y) cos(x−y)
=
sin[(x+y)+(x−y)]
cos2x•cos2y−sin2x•sin2y
=
sin2x
cos2x−(cos2x+sin2x)sin2y
=
=右.sin2x
cos2x−sin2y