`sec(arctan(3x))` Write an algebraic expression that is equivalent to the given expression. (Hint: Sketch a right triangle.)

Textbook Question

Chapter 4, 4.7 - Problem 68 - Precalculus (3rd Edition, Ron Larson).
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balajia | College Teacher | (Level 1) eNoter

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Taking 3x as oppsite side and 1 as the adjacent side,the hypotenuse will be equal to `sqrt(9x^2+1).`

So `tan^-1(3x)=sec^-1((sqrt(9x^2+1))/1)`

`sec(tan^(-1)(3x))=sec(sec^(-1)(sqrt(9x^2+1)))`

`=sqrt(9x^2+1)`

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