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Homework Help: X = sin(a)/cos(b), find da/dx

  1. Jun 6, 2010 #1
    1. The problem statement, all variables and given/known data

    x=sin(a) / cos(b)

    a+b < pi/2
    a>0, b>0

    show that

    da/dx = cos^3(b)cos(a) / cos(a+b)cos(a-b)


    3. The attempt at a solution

    dx/da = cos(a) / cos(b) therefore
    da/dx = cos(b) / cos(a)

    =cos^3(b)cos(a) / cos^2(b)cos^2(a)

    However the denominator of the desired format = cos(a+b)cos(a-b) = cos^2(a)cos^2(b)-sin^2(a)sin^2(b)

    Not sure how to get rid of the sin^2(a)sin^2(b) term...
     
  2. jcsd
  3. Jun 6, 2010 #2

    Mark44

    Staff: Mentor

    You are trying to show that cos(a+b)cos(a-b) = cos^2(b)cos^2(a). I am not able to find where you went wrong, but this equation isn't an identity.

    As a counterexample, if a = b = pi/6, cos(a) = 1/2, cos(b) = 1/2, cos(a+b) = sqrt(3)/2 and cos(a - b) = 1.

    Substituting these values into cos(a+b)cos(a-b) = cos^2(b)cos^2(a), you get sqrt(3)/2 * 1 on the left side and (1/4) * (1/4) on the right.
     
  4. Jun 7, 2010 #3

    Mark44

    Staff: Mentor

    Are you sure you copied the problem down correctly?
     
  5. Jun 7, 2010 #4
    Yes I did copy it down correctly. Obviously a mistake in the question as clearly that equality doesnt hold true

    Thanks for your validation!
     
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