（1+tanα+cotα)/(1+tan^2α+tanα)-cotα/(1+tan^2α)=sinα乘cosα麻烦帮忙证明下,
问题描述：
（1+tanα+cotα)/(1+tan^2α+tanα)-cotα/(1+tan^2α)=sinα乘cosα
麻烦帮忙证明下,
答
原式左边=(1+tanα+cotα)/(1+tan^2α+tanα)-cotα/(1+tan^2α)
=(1+tanα+1/tanα)/(1+tan^2α+tanα)-1/[tanα(1+tan^2α)]
=(tanα+tan^2α+1)/[tanα(1+tan^2α+tanα)]-1/[tanα(1+tan^2α)]
=1/[tanα-1/[tanα(1+tan^2α)]
=(1+tan^2α-1)/[tanα(1+tan^2α)]
=tanα/(1+tan^2α)…………因为sin2α=2tanα/(1+tan^2α)
=(sin2α)/2
=sinαcosα
=右边
答
（1+tanα+cotα)/(1+tan^2α+tanα)-cotα/(1+tan^2α)=cotα(tanα+tan^2α+1)/(1+tan^2α+tanα)-cotα/(1+tan^2α)=cotα(1-1/(1+tan^2α))=cotα*tan^2α/(1+tan^2α)=tanα/(1+tan^2a)=sinα/cosα*(1+sin^2α...