问题 解答题
已知tanx=2,
(1)求
cosx+sinx
cosx-sinx
的值.
(2)求2sin2x-sinxcosx+cos2x的值.
答案

(1)

cosx+sinx
cosx-sinx
=
1+tanx
1-tanx
=
1+2
1-2
=-3

(2)2sin2x-sinxcosx+cos2x=

2sin2x-sinxcosx+cos2x
sin2x+cos2x
=
2tan2x-tanx+1
tan 2x+1
=
7
5

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