sin(π/4+α)sin(π/4-α)=1/4 求2sin^2(a) -1+tana-1/tan

sin(π/4+α)sin(π/4-α)=1/4 求2sin^2(a) -1+tana-1/tan
sin(π/4+α)sin(π/4-α)=1/4 求2sin^2(a) -1+tana-1/tan

sin(π/4+α)sin(π/4-α)=1/4 求2sin^2(a) -1+tana-1/tan
sin(π/4+a)cos[π/2-(π/4-a)]=1/4
2sin(π/4+a)cos(π/4+a)=1/2
sin[2(π/4+a)]=1/2
sin(π/2+2a)=1/2
cos2a=1/2
sin²2a+cos²2a=1
所以sin2a=±√3/2
tana-1/tana
=sina/cosa-cosa/sina
=(sin²a-cos²a)/sinacosa
=-cos2a/(1/2*sin2a)
=-2cos2a/sin2a
所以原式=-cos2a-2cos2a/sin2a
=-1/2±2√3/3

sin(π/4+α)sin(π/4-α)=(2^0.5/2*sinα+2^0.5/2*cosα)*(2^0.5/2*cosα-2^0.5/2*sinα)=0.5*((cosα)^2-(sinα)^2)=0.5*cos(2α)=1/4
所以cos(2α)=0.5
sin(2α)=±3^0.5/2
tan(2α)=±3^0.5
2sin^2(α) -1+tanα-1/t...

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sin(π/4+α)sin(π/4-α)=(2^0.5/2*sinα+2^0.5/2*cosα)*(2^0.5/2*cosα-2^0.5/2*sinα)=0.5*((cosα)^2-(sinα)^2)=0.5*cos(2α)=1/4
所以cos(2α)=0.5
sin(2α)=±3^0.5/2
tan(2α)=±3^0.5
2sin^2(α) -1+tanα-1/tanα=(sinα)^2-(cosα)^2+((tanα)^2-1)/tanα
=-cos(2α)+((sinα)^2-(cosα)^2)/sinα*cosα
=-cos(2α)+(-cos(2α))/(0.5*sin(2α))=-0.5+(-0.5)/(±0.5*3^0.5/2)=-0.5±2*3^0.5/3

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