若A-B=π/6,tanA-tanB=2√3/3,求cosAcosB=_____
问题描述:
若A-B=π/6,tanA-tanB=2√3/3,求cosAcosB=_____
答
tanA-tanB=sinA/cosA-sinB/cosB=(sinAcosB-sinBcosA)/(cosAcosB)=sin(A-B)/(cosAcosB)=sin(π/6)/(cosAcosB)=1/(2cosAcosB)=2√3/3=2/√32cosAcosB=√3/2cosAcosB=√3/4