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Prove that the equation is an identity. State any restrictions.

  1. Jan 11, 2013 #1
    1. The problem statement, all variables and given/known data

    cos(x)^2/(1+3sin(x)-4sin(x)^2)=(1+sin(x))/(1+4sin(x))


    2. Relevant equations
    We are taking a topic in math where you rearrange one side of the formula to match the other


    3. The attempt at a solution
    I have factor 1+3sin(x)-4sin(x)^2 to get (-sin(x)+1)(4sin(x)+1)
     
  2. jcsd
  3. Jan 11, 2013 #2

    jedishrfu

    Staff: Mentor

    if you rewrite 1 + 3 sin x -4 (sin x)^2 using u-sin x you get the quadratic - 4 u^2 + 3u +1 which is fairly easy to factor.
     
  4. Jan 11, 2013 #3

    Mark44

    Staff: Mentor

    Continue working on the left side of your equation. What can you do with cos2(x). There's an identity you can use to change it.

    The factors you found for the denominator are correct, but it would be better to write them as (1 - sin(x))(1 + 4sin(x)).
     
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