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

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Answer 1 · 2016-05-28T06:28:34

proved

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

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

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

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

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

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