已知tanx=2,则3sin2x+2cos2xcos2x-3sin2x的值为 ___ .
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已知tanx=2,则
3sin2x+2cos2x |
cos2x-3sin2x |
∵tanx=2,
则
3sin2x+2cos2x
cos2x-3sin2x=
6sinxcosx+2(cos2x-sin2x)
cos2x-sin2x-6sinxcosx
=
6sinxcosx
sin2x+cos2x+2×
cos2x-sin2x
cos2x+sin2x
cos2x-sin2x-6sinxcosx
sin2x+cos2x
=
6tanx
1+tan2x+2×
1-tan2x
1+tan2x
1-tan2x-6tanx
1+tan2x
=-0.4
则
3sin2x+2cos2x
cos2x-3sin2x=
6sinxcosx+2(cos2x-sin2x)
cos2x-sin2x-6sinxcosx
=
6sinxcosx
sin2x+cos2x+2×
cos2x-sin2x
cos2x+sin2x
cos2x-sin2x-6sinxcosx
sin2x+cos2x
=
6tanx
1+tan2x+2×
1-tan2x
1+tan2x
1-tan2x-6tanx
1+tan2x
=-0.4
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