已知tan(π/4 +α)=-1/2 试求式子 (sin2α-2cos^2）/（1+tanα）的值
问题描述：
已知tan(π/4 +α)=-1/2 试求式子 (sin2α-2cos^2）/（1+tanα）的值
答
tan(π/4 +α)=(tanπ/4+tanα)/(1-tanπ/4*tanα)=(1+tanα)/(1-tanα)=-1/2所以tanα=-3sinα/cosα=tanα=-3sinα=-3cosα代入(sinα)^2+(cosα)^2=1(sinα)^2=9/10(cosα)^2=1/10sinα/cosα=-3