text: Equation
  
  • Mar 11th 2011, 11:19 AM
  Critter314
  Equation
  How to prove?
  $cos 2x + cos x = sin^2 x$
  All Ive got so far is $cos^2 x - sin^2 x + cos x = sin^2 x$
  • Mar 11th 2011, 11:23 AM
  emakarov
  Let's see, cos(2 * 0) + cos(0) = 2. Hmm...
  • Mar 11th 2011, 11:36 AM
  TheChaz
  Now substitute $\displaystyle \sin^2{x} = 1 - \cos^2{x}$ to get a quadratic equation in $\displaystyle \cos{x}$, which you will be able to solve.
explanation: The document contains a math question and a series of responses that provide hints or partial solutions to the question. The initial post asks how to prove the equation \( \cos 2x + \cos x = \sin^2 x \), and subsequent posts offer suggestions and counterexamples.
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: Equation
  
  • Mar 11th 2011, 11:19 AM
  Critter314
  Equation
  How to prove?
  $cos 2x + cos x = sin^2 x$
  All Ive got so far is $cos^2 x - sin^2 x + cos x = sin^2 x$
  • Mar 11th 2011, 11:23 AM
  emakarov
  Let's see, cos(2 * 0) + cos(0) = 2. Hmm...
  • Mar 11th 2011, 11:36 AM
  TheChaz
  Now substitute $\displaystyle \sin^2{x} = 1 - \cos^2{x}$ to get a quadratic equation in $\displaystyle \cos{x}$, which you will be able to solve.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a series of responses that provide hints or partial solutions to the question. The initial post asks how to prove the equation \( \cos 2x + \cos x = \sin^2 x \), and subsequent posts offer suggestions and counterexamples.
  
  Label: question-and-answer