若(1+tanα)/(1-tanα)=2013,则1/(cos2α+tan2α)=?

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若(1+tanα)/(1-tanα)=2013,则1/(cos2α+tan2α)=?若(1+tanα)/(1-tanα)=2013,则1/(cos2α+tan2α)=?若(1+tanα)/(1-tan

若(1+tanα)/(1-tanα)=2013,则1/(cos2α+tan2α)=?
若(1+tanα)/(1-tanα)=2013,则1/(cos2α+tan2α)=?

若(1+tanα)/(1-tanα)=2013,则1/(cos2α+tan2α)=?
(1+tanα)/(1-tanα)=2013
1+tanα=2013-2013tanα
tanα=2012/2014=1006/1007
cos2α=cosα^2-sinα^2
=(cosα^2-sinα^2)/(cosα^2+sinα^2)
=(1-tanα^2)/(1+tanα^2)
tan2α=2tanα/(1-tanα^2)
接下来代入计算很繁,是不是写错题目了?
如果题目是1/cos2α+tan2α就好算
1/cos2α+tan2α
=(1+tanα^2)/(1-tanα^2)+2tanα/(1-tanα^2)
=(1+tanα^2+2tanα/(1-tanα^2)
=(1+tanα)^2/[(1-tanα0(1+tanα)]
=(1+tanα)/(1-tanα)=2013

由前一式解方程,求出tana = 2012/2014 = 1006/1007
再对cos2a tan2a用万能公式代换即可求解