lim tanx-sinx/sin^2x x趋近于0,x的极限

(tanx-sinx)/sin²x
=(sinx/cosx-sinx)/sin²x
=(1/cosx-1)/sinx
=(1-cosx)/sinacosx
x趋于0
所以1-cosx~x²/2
sinx~x
所以原式=lim(x²/2)/xcosx
=limx/(2cosx)
=0