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

Explanation

To prove that

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

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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