tan(π/4-θ)等于多少
tan(π/4-θ)+tan(π/4+θ)=4且-π<θ<-π/2求sin^2θ-2sinθcosθ-cos^2θ的值...
tan(π/4-θ)+tan(π/4+θ)=4 且-π<θ<-π/2 求sin^2θ-2sinθcosθ-cos^2θ的值
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tan(π/4-θ)=(tanπ/4-tanθ)/(1+tanπ/4*tanθ)=(1-tanθ)/(1+tanθ)
tan(π/4+θ)=(tanπ/4+tanθ)/(1-tanπ/4*tanθ)=(1+tanθ)/(1-tanθ)
tan(π/4-θ)+tan(π/4+θ)=(1-tanθ)/(1+tanθ)+(1+tanθ)/(1-tanθ)
=2(1+tan^2θ)/(1-tan^2θ)=4
所以1+tan^2θ=2(1-tan^2θ)
3tan^2θ=1
tan^2θ=1/3
因为-π
tan(π/4+θ)=(tanπ/4+tanθ)/(1-tanπ/4*tanθ)=(1+tanθ)/(1-tanθ)
tan(π/4-θ)+tan(π/4+θ)=(1-tanθ)/(1+tanθ)+(1+tanθ)/(1-tanθ)
=2(1+tan^2θ)/(1-tan^2θ)=4
所以1+tan^2θ=2(1-tan^2θ)
3tan^2θ=1
tan^2θ=1/3
因为-π
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