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Lim tan 2x - sin 2x
x->0​

1 Answer

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By definition of tangent,


\tan x=(\sin x)/(\cos x)

So


\displaystyle\lim_(x\to0)(\tan2x-\sin2x)=\lim_(x\to0)\sin2x\left(\frac1{\cos2x}-1\right)


\displaystyle=\left(\lim_(x\to0)\sin2x\right)\left(\lim_(x\to0)\left(\frac1{\cos2x}-1\right)\right)=0

User Mgrim
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