text: # `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).
  See all solutions for this textbook.
  
  balajia | College Teacher | (Level 1) eNoter
  
  Posted on
  
  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)`