已知(1+tan2α)/(1-tanα)=2010,求(1/cos2α)+tan2α

题目

已知(1+tan2α)/(1-tanα)=2010,求(1/cos2α)+tan2α

答案

（1+tan2α）/（1-tanα）=2010
=>{1+2tanα/[(1-tanα)^2]}/(1-tanα)
=1-(tanα)^2+2tanα=2010(1+tanα)
=>2009+(tanα)^2+2008tanα=0 (1)
=>(1+tanα)=[tanα-(tanα)^2]/2009
1/cos2α+tan2α=(1+sin2α)/cos2α=(1+tanα)/(1-tanα)=tanα/2009
根据(1)可求出tanα~=-1,-2007,就可求出上式～=-1/2009 或者-2007/2009.