证明(tan^2a+tana+1)(cot^2a+cota+1)=tan^2a+cot^2a+1

(tan^2a+tana+1)(cot^2a+cota+1)中应该是
(tan^2a+tana+1)(cot^2a-cota+1)=tan^2a+cot^2a+1
tan^2a+cot^2a+1
=tan^2a+1/tan^2a+1
=(tana+1/tana)^2-1
=(tana+1/tana+1)(tana+1/tana-1)
=(tan^2a+tana+1))[(tana+1/tana-1)/tana]
=(tan^2a+tana+1)(1+1/tan^2a-1/tana)
=(tan^2a+tana+1)(cot^2a-cota+1)