Question

Prove the following identity

Answer 1

LHS

cosA-sinA+1/CosA+sinA-1

Divide by sinA

cotA-1+CosecA/cotA+1-CosecA

On rearranging

cotA+cosecA-1/cotA-cosecA+1

Using the identity

1+cot2A=cosec2A

cotA+cosecA-(cosec²A-cot²A)/cotA-cosecA+1

cotA+CosecA-[(cosecA+cotA)(cosecA-cotA) ]/cotA-cosecA+1

taking CotA+CosecA common

CotA+CosecA(1-cosecA+CotA)/cotA-CosecA+1

on cancelling the terms we get..

CotA+CosecA=RHS

Hence proved!!

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Answer 2

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