若sinα+cosα=2/3,求(√2sin(2α-π/4)+1)/(1+tanα)的值.

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若sinα+cosα=2/3,求(√2sin(2α-π/4)+1)/(1+tanα)的值.
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若sinα+cosα=2/3,求(√2sin(2α-π/4)+1)/(1+tanα)的值.
若sinα+cosα=2/3,求(√2sin(2α-π/4)+1)/(1+tanα)的值.

若sinα+cosα=2/3,求(√2sin(2α-π/4)+1)/(1+tanα)的值.
结论:-5/9
由sinα+cosα=2/3 得sin2α=-5/9
1+tanα=1+(1-cos2α)/sin2α=(sin2α-cos2α+1)/sin2α
√2sin(2α-π/4)+1=sin2α-cos2α+1
(√2sin(2α-π/4)+1)/(1+tanα)=sin2α=-5/9 
希望对你有点帮助!

结论:-5/9

  1. 由sinα+cosα=2/3 得sin2α=-5/9

  2. 1+tanα=1+(1-cos2α)/sin2α=(sin2α-cos2α+1)/sin2α

    √2sin(2α-π/4)+1=sin2α-cos2α+1

  3. (√2sin(2α-π/4)+1)/(1+tanα)=sin2α=-5/9 

    希望对你有点帮助!