text: # if sinx+sin2x=2then find,cos2x+cos4x
  
  Vinay Arya
  37 Points
  13 years ago
  
  Hi Vishwa Sharma
  
  sinx+sin2x=2
  
  =>sinx+sin2x-2=0
  
  =>(sinx-1)(sinx+2)=0
  
  =>sinx=1 or sinx=-2
  
  We know that sinx cannot be equal to -2.Hence rejaecting sinx=-2
  
  Therefore, sinx=1 =>x=pi/2
  
  cos2x+cos4x=xos2pi/2 + cos4pi/2 =0
  
  Chaitanya Borah
  34 Points
  13 years ago
  
  sinx+sin2x=2
  
  =>sinx=1+1-sin2x
  
  =>sinx=1+cos2x
  
  =>cos2x=sinx-1
  
  now,
  
  cos2x+cos4x
  
  =cos2x+(sinx-1)2
  
  =cos2x+sin2x-2sinx+1
  
  =1-2sinx+1
  
  =2(1-sinx)
explanation: The document contains a math question and multiple answers to the question. The question is about finding the value of \( \cos 2x + \cos 4x \) given that \( \sin x + \sin 2x = 2 \). Two different users, Vinay Arya and Chaitanya Borah, provide their solutions to the problem.
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: # if sinx+sin2x=2then find,cos2x+cos4x
  
  Vinay Arya
  37 Points
  13 years ago
  
  Hi Vishwa Sharma
  
  sinx+sin2x=2
  
  =>sinx+sin2x-2=0
  
  =>(sinx-1)(sinx+2)=0
  
  =>sinx=1 or sinx=-2
  
  We know that sinx cannot be equal to -2.Hence rejaecting sinx=-2
  
  Therefore, sinx=1 =>x=pi/2
  
  cos2x+cos4x=xos2pi/2 + cos4pi/2 =0
  
  Chaitanya Borah
  34 Points
  13 years ago
  
  sinx+sin2x=2
  
  =>sinx=1+1-sin2x
  
  =>sinx=1+cos2x
  
  =>cos2x=sinx-1
  
  now,
  
  cos2x+cos4x
  
  =cos2x+(sinx-1)2
  
  =cos2x+sin2x-2sinx+1
  
  =1-2sinx+1
  
  =2(1-sinx)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and multiple answers to the question. The question is about finding the value of \( \cos 2x + \cos 4x \) given that \( \sin x + \sin 2x = 2 \). Two different users, Vinay Arya and Chaitanya Borah, provide their solutions to the problem.
  
  Label: question-and-answer