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Homework Help: Show what happens to 'U' if 'a' is doubled.

  1. Apr 2, 2014 #1
    1. The problem statement, all variables and given/known data

    Demonstrate what happens to X when a is doubled (a → 2a).

    a = tan^2(X) - 1/cos^2(X)

    2. Relevant equations

    None given formally;
    Pythagorean Theorem - sin^2(θ) + cos^2(θ) = 1 (added myself).

    3. The attempt at a solution

    Divide through Pythagorean above to give: tan^2(θ) + 1 = 1/cos^2(θ)
    1/cos^2(θ) = sec^2(θ).
    tan^2(θ) - sec^2(θ) = -1

    From given equation, a = -1.

    Doubling a yields 2a.
    But tan^2(θ) - sec^2(θ) = -1 for all values of (θ) including X as given.

    Is my solution therefore that nothing happens to X if a is doubled, or does the solution not consist of using the pythagorean identity?

    All thanks appreciated.
  2. jcsd
  3. Apr 2, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper

    You have it right. a=(-1) is the only solution. You can't really even talk about what happens to X when a=(-2), then there are no solutions for X.
  4. Apr 2, 2014 #3


    Staff: Mentor

    Looks fine, if a bit long-winded.
    You're given a = tan2(x) - 1/cos2(x)
    The right side can be written as tan2(x) - sec2(x) = tan2(x) - (tan2(x) + 1) = tan2(x) - tan2(x) - 1 = -1

    So a = -1 identically for all values of x for which tan(x) is defined and cos(x) ≠ 0.

    Doubling a has no effect on x.
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