若A-B=π/6,tanA-tanB=2√3/3,求cosAcosB=_____

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若A-B=π/6,tanA-tanB=2√3/3,求cosAcosB=_____

若A-B=π/6,tanA-tanB=2√3/3,求cosAcosB=_____
若A-B=π/6,tanA-tanB=2√3/3,求cosAcosB=_____

若A-B=π/6,tanA-tanB=2√3/3,求cosAcosB=_____
tanA-tanB
=sinA/cosA-sinB/cosB
=(sinAcosB-sinBcosA)/(cosAcosB)
=sin(A-B)/(cosAcosB)
=sin(π/6)/(cosAcosB)
=1/(2cosAcosB)
=2√3/3=2/√3
2cosAcosB=√3/2
cosAcosB=√3/4