搜搜考试网已知tanx=2(1)求(2/3)sin^2x+(1/4)cos^2x的值
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已知tanx=2(1)求(2/3)sin^2x+(1/4)cos^2x的值
（2）求2sin^x-sinxsosx+cos^2x的值
（2）求2sin^x-sinxsosx+cos^2x的值
tanx=2
平方得
sin²x=4cos^2x
5cos^2x=1 cos^2x=1/5
sin^2x=4/5
sinxcosx=√[sin^2xcos^2x]=2/5
(2/3)sin^2x+(1/4)cos^2x
=(8/12)sin^2x+(3/12)cos^2x
=(3/12)[sin^2x+cos^2x]+(5/12)sin^2x
=(3/12)+(5/12)sin^2x
=3/12+(5/12)*(4/5)
=7/12
2sin^x-sinxsosx+cos^2x
=1+sin²x-sinxcosx
=1+4/5-2/5
=7/5
平方得
sin²x=4cos^2x
5cos^2x=1 cos^2x=1/5
sin^2x=4/5
sinxcosx=√[sin^2xcos^2x]=2/5
(2/3)sin^2x+(1/4)cos^2x
=(8/12)sin^2x+(3/12)cos^2x
=(3/12)[sin^2x+cos^2x]+(5/12)sin^2x
=(3/12)+(5/12)sin^2x
=3/12+(5/12)*(4/5)
=7/12
2sin^x-sinxsosx+cos^2x
=1+sin²x-sinxcosx
=1+4/5-2/5
=7/5
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