Prove that : `(sectheta+tantheta-1)/(tantheta-sectheta+1)=(costheta)/(1-sintheta)`

Explanation

To prove the identity:

\[ \frac{\sec \theta + \tan \theta - 1}{\tan \theta - \sec \theta + 1} = \frac{\cos \theta}{1 - \sin \theta} \]

we will start with the left-hand side (LHS) and manipulate it to show that it equals the right-hand side (RHS).

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