Arre, you start with 1 + tan² A and just replace tan A with sin A/cos A. Combine it all over the common denominator, use sin² A + cos² A = 1, and there you have 1/cos² A, which is sec² A. Done. My old CBSE notes are smudged right at that line from going over it so many times, practicing for my second attempt. It’s a small, neat proof—unlike my life, which has never been proven in one clean step.
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