Derivative of Tan(x) Proof (Using the Limit Definition)

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Proof that the derivative of tan(x) is sec^2(x) using the limit definition of the derivative.
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Whenever you see trig terms squared, there's probably an identity to be used. It's all the pythagorean theorem

marcushendriksen
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Is it possible to solve it without using sinx/cosx?

maxstirner