若tan(a+3π/4)=2011,则1/cos2a+tan2a=?没思路,
问题描述：
若tan(a+3π/4)=2011,则1/cos2a+tan2a=?没思路,
答
tan(a+3π/4)=(tana-1)/(tana+1)=2011
1/cos2a+tan2a
=1/cos2a+sin2a/cos2a
=(1+sin2a)/cos2a
=(sina+cosa)^2/(cos^2a-sin^2a)
=(cosa+sina)/(cosa-sina)
=(1+tana)/(1-tana)
=-(tana+1)/(tana-1)
=-1/2011为什么要写成(tana-1)/(tana+1)？tan(a+3π/4)=(tana-1)/(tana+1)=2011两角和的正切公式 tan3π/4=-1