将1化为cos²α+sin²α,移项合并,并将两边除以cosα.cos²α+3sinαcosα-4sin²α=0,1+3tanα-4(tanα)^2=04(tanα)^2-3tanα-1=0(4tanα+1)(tanα-1)=0tanα=-1/4或tanα=1.