求极限lim(x-->0) (tanX-sinX)/[(sin^3)X]

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求极限lim(x-->0)(tanX-sinX)/[(sin^3)X]求极限lim(x-->0)(tanX-sinX)/[(sin^3)X]求极限lim(x-->0)(tanX-sinX)/[(sin

求极限lim(x-->0) (tanX-sinX)/[(sin^3)X]
求极限lim(x-->0) (tanX-sinX)/[(sin^3)X]

求极限lim(x-->0) (tanX-sinX)/[(sin^3)X]
(tanx-sinx)/sin³x
=(sinx/cosx-sinx)/sin³x
=(1/cosx-1)/sin²x
=[(1-cosx)/cosx]/(1-cos²x)
=1/[cosx(1+cosx)]
所以极限=1/[1*(1+1)]=1/2