Question

How do you prove `((1+tanx)/(1-tanx)) + ((1+cotx)/(1-cotx)) = 0`?

Answer 1

proved

Explanation:

`LHS=((1+tanx)/(1-tanx)) + ((1+cotx)/(1-cotx))`

`=((1+tanx)/(1-tanx)) + ((1+cotx)/(1-cotx))*tanx/tanx`

`=((1+tanx)/(1-tanx)) + ((tanx+cotx*tanx)/(tanx-cotx*tanx))`

`=((1+tanx)/(1-tanx)) + ((tanx+1)/(tanx-1))`

`=((1+tanx)/(1-tanx))- ((1+tanx)/(1-tanx))=0=RHS`