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](/uploads/image/z/618118-70-8.jpg?t=%E5%B7%B2%E7%9F%A5tan%28%CF%80%2F4+%2B%CE%B1%29%3D-1%2F2+%E8%AF%95%E6%B1%82%E5%BC%8F%E5%AD%90+%28sin2%CE%B1-2cos%5E2%EF%BC%89%2F%EF%BC%881%2Btan%CE%B1%EF%BC%89%E7%9A%84%E5%80%BC)
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
=(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
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