若(1+tanα)/(1-tanα)=2003,则1/cos2α+tan2α=

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若(1+tanα)/(1-tanα)=2003,则1/cos2α+tan2α=若(1+tanα)/(1-tanα)=2003,则1/cos2α+tan2α=若(1+tanα)/(1-tanα)=200

若(1+tanα)/(1-tanα)=2003,则1/cos2α+tan2α=
若(1+tanα)/(1-tanα)=2003,则1/cos2α+tan2α=

若(1+tanα)/(1-tanα)=2003,则1/cos2α+tan2α=
注:不知原题是要求解(1/cos2α)+tan2α=?还是要求解1/(cos2α+tan2α)=?我就把两种结果都求解出来.
∵(1+tanα)/(1-tanα)=2003 ==>1+tanα=2003(1-tanα)
==>2004tanα=2002
==>tanα=2002/2004=1001/1002
∴cos2α=(cos²α-sin²α)/(cos²α+sin²α)
=(1-tan²α)/(1+tan²α)
=2003
tan2α=2tanα/(1-tan²α)
=2*(1001/1002)/[1-(1001/1002)²]
=2002*1002/2003
故(1/cos2α)+tan2α=(2002*1002+1)/2003=2006005/2003≈1001.5
1/(cos2α+tan2α)=2003/(2003²+1002*2002)=2003/6018013≈3.33×10^(-4)