已知tan﹙α+π/4﹚=2,(1)求(4sinα-2cosα)/(5sin²α+3cosα)的值;(2)求2sin²α+4sinαcosα的值
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已知tan﹙α+π/4﹚=2,(1)求(4sinα-2cosα)/(5sin²α+3cosα)的值;(2)求2sin²α+4sinαcosα的值
已知tan﹙α+π/4﹚=2,(1)求(4sinα-2cosα)/(5sin²α+3cosα)的值;
(2)求2sin²α+4sinαcosα的值
已知tan﹙α+π/4﹚=2,(1)求(4sinα-2cosα)/(5sin²α+3cosα)的值;(2)求2sin²α+4sinαcosα的值
∵tan﹙α+π/4﹚=2
∴(tanα+1)/(1-tanα)=2
∴tanα+1=2-2tanα
∴tanα=1/3
∴sinα/cosα=1/3,cosα=3sinα
又sin²α+cos²α=1
∴sin²α=1/10
(1)(4sinα-2cosα)/(5sinα+3cosα)的\
=(4sinα-6sinα)/(5sinα+9sinα)
=-2/14=-1/7
(2)2sin²α+4sinαcosα
=2*1/10+12sin²α
=2/10+12/10=14/10=7/5
tan﹙α+π/4﹚=2
=(1+tana)/(1-tana)=2
得
tana=1/3
|sina|=√10/10
|cosa|=3√10/10
(4sinα-2cosα)/(5sin²α+3cosα)
分子分母同时除以cosa得
=(4tana-2)/(5sinatana+3)
=(4/3-2)/[(5/3)si...
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tan﹙α+π/4﹚=2
=(1+tana)/(1-tana)=2
得
tana=1/3
|sina|=√10/10
|cosa|=3√10/10
(4sinα-2cosα)/(5sin²α+3cosα)
分子分母同时除以cosa得
=(4tana-2)/(5sinatana+3)
=(4/3-2)/[(5/3)sina+3]
sina=√10/10时
=(-2/3)/[(√10/6)+3]
=-4/(√10+18)
sina=-√10/10时
=(-2/3)/[(-√10/6)+3]
=(-4)/(-√10+18)
2sin²α+4sinαcosa
=1/5+12/10
=7/5
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