`(cota)/(1-cota)+(tana)/(1-tana)=-1`
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Answer:
TanA/1-cotA)+(cotA/1-tanA)=1+tanA+cotA
Let us start with LHS
= 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
= RHS
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