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