Prove the following identities: `tan^2A-tan^2B=(cos^2B-cos^2A)/(cos^2Bcos^2A)=(sin^2A-sin^2B)/(cos^2Acos^2B)` `(sinA-sinB)/(cosA+cosB)+(cosA-cosB)/(sinA+sinB)=0`

Explanation

To prove the given identities, we will break down each part step by step.

### Identity 1:
Prove that
\[ \tan^2 A - \tan^2 B = \frac{\cos^2 B - \cos^2 A}{\cos^2 B \cos^2 A} = \frac{\sin^2 A - \sin^2 B}{\cos^2 A \cos^2 B} \]

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