Question

Lim x tends to 0 tan2x-sin2x
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Sin^33x

Answer 1

$\binom{lim}{x.. > 0} \frac{ \tan(2x) }{2x} \times 2 - \binom{lim}{x...0} \frac{ \sin(2x) }{2x} \times 2 \\ \\ = (1 \times 2) - (1 \times 2) \\ \\ = 0$
0

hence zero is the answer