How can I find the limit of given trigonometric function? I am messed up on solving this question. What should I do first in order to get the answer ?
This is the trigonometric function
$$ \lim \limits_{x \rightarrow 0} \frac{(a+x)\sec(a+x) - a \sec(a)}{x} $$

One solution, if allowed, uses Taylor series.
Built a round $x=0$, $$\sec(a+x)=\sec (a)+x \tan (a) \sec (a)+O\left(x^2\right)$$ $$(x+a)\sec(a+x)=a \sec (a)+x (\sec (a)+a \tan (a) \sec (a))+O\left(x^2\right)$$
