Limit tanx-sinx/x3 when x approaches 0

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Why the limit of (tanx - sinx)/x³ ≠ 0?
lim x-0 (tanx-sinx)/x^3 =1/2
Find the limit of tanx-sinx/x3 as x approaches 0 without using the L'Hôpital's rule (L'Hopital's rule).

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