(sinθ+tanθ)/(cosθ+cotθ)
=[tanθ(cosθ+1)]/[cotθ(sinθ+1)]
=(tanθ)^2[(cosθ+1)/(sinθ+1)]
θ≠kπ/2
(tanθ)^2恒为正
cosθ+1恒为正
sinθ+1恒为正
原式恒取正值