用等价无穷小来做
因为x→0
lim tan(sinx)/sinx
换元t=sinx
=lim(t→0) tant / t
=lim sint/t * lim 1/cost
=1*1
=1
因此,tan(sinx)~sinx
lim sin(tanx)/tanx
换元t=tanx
=lim(t→0) sint/t
=1
那么,sin(tanx)~tanx
故,
lim tan(sinx)/sin(tanx)
=lim sinx/tanx
=lim sinx/(sinx/cosx)
=lim cosx
=1
有不懂欢迎追问