解：tanα/（tanα-1）=-1tanα=-tanα+12tanα=1tanα=1/2sin²α+sinαcosα+2=(sin²α+sinαcosα)/(sin²α+cos²α)+2 前面的分式分子分母同时除以cos²α=(tan²α+tanα)/(tan²α+1) +2=(1/4+1/2)(1/4+1)+2=3/5+2=13/5
