Question

Lim tan 2x - sin 2x
x->0​

Answer 1

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`