∵ tanβ=sinβ/cosβ∴(sinβ)^2=48(1-sin^2β) sinβ=4√3/7 ∴cosβ=√(1-sin^2β)=1/7∵sin(α+β)=√[1-cos^2(α+β)]=5√3/14∴cosα=cos(α+β-β)=cos(α+β)cosβ+sin(α+β)sinβ=1/2