Prove that `(cos theta-sintheta)/(cos theta+sintheta)=sec 2 theta-tan 2theta`.

Explanation

To prove that

\[ \frac{\cos \theta - \sin \theta}{\cos \theta + \sin \theta} = \sec 2\theta - \tan 2\theta, \]

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

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