Answer
Set $f(0)=1$
Work Step by Step
Step 1. Find the limit $\lim_{x\to0}\frac{tan(tan(x))}{sin(sin(x))}=\lim_{x\to0}\frac{sin(tan(x))}{sin(sin(x))}\frac{1}{cos(tan(x))}=\lim_{x\to0}\frac{sin(tan(x))}{tan(x)}\frac{tan(x)}{sin(sin(x))}(1)=\lim_{x\to0}(1)\frac{sin(x)}{sin(sin(x))}\frac{1}{cos(x)}=(1)(1)=1$
Step 2. To extend the functions to be continuous at the origin, we need to set $f(0)=1$
