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Prove that: (tanA+ sec A-1)/(tan A-sec...

Prove that:
`(tanA+ sec A-1)/(tan A-secA+1)=(cosA)/(1-sinA)`

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To prove the identity \[ \frac{\tan A + \sec A - 1}{\tan A - \sec A + 1} = \frac{\cos A}{1 - \sin A}, \] we will start with the left-hand side (LHS) and simplify it step by step. ...
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