Determine the following limit: $$ y=\lim _{x \rightarrow 0} \frac{\tan x-x}{x-\sin x} $$

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Calculate the limit $$ \lim_{x ightarrow 0} \frac{	an x-x}{x-\sin x} $$.
Evaluate the limit by following steps:
- step0: Evaluate using L'Hopital's rule:
  $$\lim _{xightarrow 0}\left(\frac{	an\left(xight)-x}{x-\sin\left(xight)}ight)$$
- step1: Use the L'Hopital's rule:
  $$\lim _{xightarrow 0}\left(\frac{\frac{d}{dx}\left(	an\left(xight)-xight)}{\frac{d}{dx}\left(x-\sin\left(xight)ight)}ight)$$
- step2: Find the derivative:
  $$\lim _{xightarrow 0}\left(\frac{\sec^{2}\left(xight)-1}{1-\cos\left(xight)}ight)$$
- step3: Simplify the expression:
  $$\lim _{xightarrow 0}\left(\frac{1+\cos\left(xight)}{\cos^{2}\left(xight)}ight)$$
- step4: Rewrite the expression:
  $$\frac{\lim _{xightarrow 0}\left(1+\cos\left(xight)ight)}{\lim _{xightarrow 0}\left(\cos^{2}\left(xight)ight)}$$
- step5: Calculate:
  $$\frac{2}{\lim _{xightarrow 0}\left(\cos^{2}\left(xight)ight)}$$
- step6: Calculate:
  $$\frac{2}{1}$$
- step7: Calculate:
  $$2$$
The limit of the expression $$\frac{	an x-x}{x-\sin x}$$ as $$x$$ approaches 0 is 2.
The limit is 2.

Determine the following limit:

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