Prove that: tanA /1- cotA + cotA / 1-tanA= 1+ tanA + cotA
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Step-by-step explanation:
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)
= tan²A/tanA-1 - 1/tanA(tanA-1)
= tan³A-1/tanA(tanA-1)
= (tanA-1)(tan^²A+1+tanA)/tanA(tanA-1)
= tan²A/tanA + 1/tanA + tanA/tanA
= tanA + cotA + 1
= 1+ tanA + cotA = R.H.S
Hope it help you.
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