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Verifying Trig Identity

  1. Dec 21, 2009 #1
    1. The problem statement, all variables and given/known data

    sec^2(x) tan^2(x) + sec^2(x) = sec^4(x)

    2. Relevant equations

    sin^2 + cos^2 = 1
    1+tan^2 = sec^2
    1+cot^2 = csc^2

    3. The attempt at a solution

    First, I changed everything to sin and cos to try and make it clearer.

    1/cos^2 * sin^2/cos^2 + 1/cos^2 = sec^4
    sin^2/cos^4 + 1/cos^2

    Then I multiplied by the common denominator, cos^2

    sin^2 * cos^2/cos^6 + cos^2/cos^4

    Where do I go from here??
  2. jcsd
  3. Dec 21, 2009 #2
    You don't need to multiply the first term by cos2x/cos2, just the second so they have a common denominator. Then add the fractions and use an identity.
  4. Dec 22, 2009 #3


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    Homework Helper

    You don't need to change everything into sinx and cosx to makes things clearer. Even if you can't think about what secx is without thinking of 1/cosx you can still solve this problem:

    Set the equation to 0, then factorize by a common factor which should obviously be [itex]sec^2x[/itex]. Now use an identity.
    At this point, if you're confused about what has happened just think about this: for the equation x-x=0, you can have any value of x to satisfy the equation. This means all x values are the equation's solutions.

    But also remember that [itex]0/0\neq 0[/itex] so make sure to show that the solutions to [itex]cosx= 0[/itex] are excluded from the solutions in the original equation (This is from the first factor [itex]sec^2x[/itex]).
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