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Prove that (sin theta - cos theta +1)/...

Prove that
`(sin theta - cos theta +1)/(sin theta + cos theta -1) = (1)/((sec theta - tan theta)). `

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To prove that \[ \frac{\sin \theta - \cos \theta + 1}{\sin \theta + \cos \theta - 1} = \frac{1}{\sec \theta - \tan \theta}, \] we will start by simplifying the left-hand side (LHS) and show that it equals the right-hand side (RHS). ...
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