With steps prove that (TanA/1-cotA)+(cotA/1-tanA)=1+tanA+cotA
Please give all the steps clearly to understand
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Prof:
L.H.S = tanA/1-cotA + cotA/1-tanA
= tanA/1-1/tanA + 1/tanA/1-tanA
= tanA/tanA-1/tanA + 1/tanA(1-tanA)
= tan^2A/tanA-1 - 1/tanA(tanA-1)
= tan^3A-1/tanA(tanA-1)
= (tanA-1)(tan^2A+1+tanA)/tanA(tanA-1)
= tan^2A/tanA + 1/tanA + tanA/tanA
= tanA + cotA + 1
= 1+ tanA + cotA = R.H.S
Hope it help you.
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