text: Home
  
  >
  
  English
  
  >
  
  Class 11
  
  >
  
  Maths
  
  >
  
  Chapter
  
  >
  
  Transformation Formulae
  
  >
  
  If sintheta=n"sin"(theta+2alp...
  
  Updated On: 27-06-2022
  
  Get Answer to any question, just click a photo and upload the photo and get the answer completely free,
  
  Text Solution
  
  Solution : Given <br> sintheta=nsin(theta+2alpha)<br> =>(sintheta)/(sin(theta+2alpha))=n <br> apply componendo dividendo rule,<br> =>(sintheta+sin(theta+2alpha))/(sintheta−sin(theta+2alpha))=(n+1)/(n-1)<br> applying sinC+sinD=2sin((C+D)/2)cos((C-D)/2) and sinC−sinD=2sin((C-D)/2)cos((C+D)/2) formula<br> =>(2sin(theta+alpha)cosalpha)/(2sinalphacos(theta+alpha))=(n+1)/(n-1)<br> =>(tan(theta+alpha))/(tanalpha)=(n+1)/(n-1)<br> =>tan(theta+alpha)=(n+1)/(n-1)tanalpha
explanation: The document is a math problem and its solution. It starts with a given trigonometric equation and proceeds to solve it step-by-step using trigonometric identities and the componendo dividendo rule. The document contains both a question and an answer.
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: Home
  
  >
  
  English
  
  >
  
  Class 11
  
  >
  
  Maths
  
  >
  
  Chapter
  
  >
  
  Transformation Formulae
  
  >
  
  If sintheta=n"sin"(theta+2alp...
  
  Updated On: 27-06-2022
  
  Get Answer to any question, just click a photo and upload the photo and get the answer completely free,
  
  Text Solution
  
  Solution : Given <br> sintheta=nsin(theta+2alpha)<br> =>(sintheta)/(sin(theta+2alpha))=n <br> apply componendo dividendo rule,<br> =>(sintheta+sin(theta+2alpha))/(sintheta−sin(theta+2alpha))=(n+1)/(n-1)<br> applying sinC+sinD=2sin((C+D)/2)cos((C-D)/2) and sinC−sinD=2sin((C-D)/2)cos((C+D)/2) formula<br> =>(2sin(theta+alpha)cosalpha)/(2sinalphacos(theta+alpha))=(n+1)/(n-1)<br> =>(tan(theta+alpha))/(tanalpha)=(n+1)/(n-1)<br> =>tan(theta+alpha)=(n+1)/(n-1)tanalpha
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a math problem and its solution. It starts with a given trigonometric equation and proceeds to solve it step-by-step using trigonometric identities and the componendo dividendo rule. The document contains both a question and an answer.
  
  Label: question-and-answer