Question

How do you rewrite `sec^2 (tan^{-1} x)` in terms of x?

Answer 1

Let

`theta =tan^{-1}x Leftrightarrow tan theta=x`.

So,

`sec^2(tan^{-1}x)=sec^2theta=1+tan^2theta=1+x^2`.

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I hope that this was helpful.