Question

1+tanx/1+cotx=tanx

Answer 1

change tan(x) and cot(x) to their "sine" and "cosine" identity

then simplify, see what you get

Answer 2

that is \(\bf \cfrac{1+tan(x)}{1+cot(x)}=tan(x)
\\ \quad \\
\cfrac{1+tan(x)}{1+cot(x)}\implies \cfrac{1+\frac{sin(x)}{cos(x)}}{1+\frac{cos(x)}{sin(x)}}\)