已知tan(π/4 +α)=-1/2 试求式子 (sin2α-2cos^2)/(1+tanα)的值

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已知tan(π/4 +α)=-1/2 试求式子 (sin2α-2cos^2)/(1+tanα)的值
已知tan(π/4 +α)=-1/2 试求式子 (sin2α-2cos^2)/(1+tanα)的值

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