原式=[(cosα)^2-(sinα)^2]*(1+tanαtan2α)=cos2α(1+tanαtan2α)=cos2α+tanαsin2α=cos2α+sinα/cosα*2sinαcosα=cos2α+2(sinα)^2=(cosα)^2-(sinα)^2+2(sinα)^2=(cosα)^2+(sinα)^2=1.