text: # Homework Help: Component Identities
  
  1. Oct 4, 2005
  
  ### brandon26
  
  Solve for x
  
  3sin(x+10)=4cos(x-10)
  
  I tried changinf everything into tan nothing out. I tried expaning the brackets and collecting like terms, that didnt work out either.
  
  2. Oct 4, 2005
  
  ### Astronuc
  
  Staff Emeritus
  3. Oct 4, 2005
  
  ### brandon26
  
  Yeh, but I cant simplify anything to solve the problem
  
  4. Oct 4, 2005
  
  ### Astronuc
  
  Staff Emeritus
  Well expand the sin and cos and apply cos (-x) = cos x, and sin (-x) = -sin x.
  
  Then collect terms/coefficients of cos x and sin x.
  
  If one has a form A cos x = B sin x, the tan x = A/B and x = tan-1 (A/B). In this problem A and B have terms of sin 10 and cos 10.
explanation: The document is a forum post from a homework help thread where a user named brandon26 is seeking assistance with solving a trigonometric equation: 3sin(x+10) = 4cos(x-10). The user describes their attempts to solve the problem, including trying to use the tangent function and expanding the brackets, but they have not been successful. Another user, Astronuc, provides guidance on how to approach the problem by expanding the sine and cosine functions and collecting like terms.
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: # Homework Help: Component Identities
  
  1. Oct 4, 2005
  
  ### brandon26
  
  Solve for x
  
  3sin(x+10)=4cos(x-10)
  
  I tried changinf everything into tan nothing out. I tried expaning the brackets and collecting like terms, that didnt work out either.
  
  2. Oct 4, 2005
  
  ### Astronuc
  
  Staff Emeritus
  3. Oct 4, 2005
  
  ### brandon26
  
  Yeh, but I cant simplify anything to solve the problem
  
  4. Oct 4, 2005
  
  ### Astronuc
  
  Staff Emeritus
  Well expand the sin and cos and apply cos (-x) = cos x, and sin (-x) = -sin x.
  
  Then collect terms/coefficients of cos x and sin x.
  
  If one has a form A cos x = B sin x, the tan x = A/B and x = tan-1 (A/B). In this problem A and B have terms of sin 10 and cos 10.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a forum post from a homework help thread where a user named brandon26 is seeking assistance with solving a trigonometric equation: 3sin(x+10) = 4cos(x-10). The user describes their attempts to solve the problem, including trying to use the tangent function and expanding the brackets, but they have not been successful. Another user, Astronuc, provides guidance on how to approach the problem by expanding the sine and cosine functions and collecting like terms.
  
  Label: question-and-answer