Question

Prove {tan A/(1-cotA)} + {cotA/(1-tanA)} = 1+tanA+cotA

Answer 1

=> tanA/(1 - cotA) + cotA/( 1 -tanA)

=>tanA/( 1-1/tanA) +1/tanA/(1 - tanA)

=>tan^2A/(tanA - 1) -1/tanA(1-tanA)

=>{ tan^3A - 1} /(tanA - 1}tanA

=>(tanA - 1)( tan^2A +tanA + 1) /tanA.(tanA- 1)

=> ( tan^2A + tanA + 1)/tanA

=>tanA + 1 + cotA

tanA + cotA + 1 = RHS