Question

Please show work along with answer:

`(1 + \tan(x) )/(1 + \cot(x) )`

Answer 1

Hello,


`(1+tan(x))/(1+cotg(x)) = (1+ (sin(x))/(cos(x)) )/(1+ (cos(x))/(sin(x))) \\\\ = (cos(x)+sin(x))/(cos(x)*( (sin(x)+cos(x))/(sin(x)) ) )\\\\ = (sin(x))/(cos(x)) \\\\ \boxed{=tan(x)}\\\\`