当0＜x＜ π /4时,函数f(x)=cosx的平方/sinxcosx- sinx的平方,求f(x)的最小值

f(x)=(cosx)^2/[sinxcosx- (sinx)^2]
=(cosx)^2/[sinxcosx+(cosx)^2-1]
=1/[tgx+1-(secx)^2]
=1/{tgx+1-[1+(tgx)^2]}
=1/[tgx-(tgx)^2]
=1/[-(tgx-1/2)^2+1/4]
>=1/[0+1/4]
=4,当且仅当tgx=1/2时取等,此时x=arctg(1/2)