Express sec2x in terms of tanx and secx

I know you have to
sec(2x) = 1/cos(2x) = 1/(cos²x - sin²x)
But how do you split that. Like how to simplify that?

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1. divide top and bottom by cos^2 (multiply by sec^2) and you have

sec^2(x)/(1-tan^2(x))

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