Question

prove that cotA/1-cotA +tanA/1-tanA =-1​

Answer 1

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

Hence Proved

Step-by-step explanation:

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