I have limit:
$$\lim_{x\to0}\left (\frac{4^{\tan(x)}+ \cos(x)}{2}\right)^{\cot(x)}$$
I tried to use the natural log:
$$\lim_{x\to 0} e^{\dfrac{\ln\left(\dfrac{4^{\tan(x)}+ \cos(x)}{2}\right)}{{\tan(x)}}}$$ But I am stuck from here, I tried multiple approaches but could not find the right result which should be $2$
How should I approach this limit?