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)`
explanation: The document contains a math question and its corresponding answer. The question asks for an algebraic expression equivalent to `sec(arctan(3x))`, and the answer provides a step-by-step solution, concluding that the expression is `sqrt(9x^2 + 1)`.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # `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)`
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its corresponding answer. The question asks for an algebraic expression equivalent to `sec(arctan(3x))`, and the answer provides a step-by-step solution, concluding that the expression is `sqrt(9x^2 + 1)`.
  
  Label: question-and-answer