Prove the following identity: `(t a ntheta+s e ctheta-1)/(t a ntheta-s e ctheta+1)=(1+sintheta)/(costheta)`

Explanation

To prove the identity

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

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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