lim┬(x→π/2) ( π/2-x) tanx =lim┬(x→π/2) ( π/2-x) sinx/cosx
=lim┬(x→π/2) [( π/2-x)/ sin(π/2-x)]*sinx
=lim┬(x→π/2) [( π/2-x)/ sin(π/2-x)]*lim┬(x→π/2)sinx
=1.
(注释：sin(π/2-x)=cosx)