lim[(sin x)^tan x],x趋向于Pai/2

lim(x->pi/2)[(sin x)^tan x]=lim(x->pi/2){[1+(sinx-1)]^[1/(sinx-1)]}^[(sinx-1)/cotx]=e^lim(x->pi/2)[(sinx-1)/cotx]=e^lim(x->pi/2)[-cosx/(cscx)^2]=e^(-0/1^2)=1