Simplifying Trigonometric Equations

  1. 1. The problem statement, all variables and given/known data
    I've been studying trig. for my Precalculus class, and I decided to give 50 problems a try, though I got stuck in two of them:

    Reduce the first expression to the second in each of the following:
    38.) cos2x-cos4x, cos2xsin2x
    and
    68.) sec4θ - sec2θ, sec2θtan2θ

    2. Relevant equations
    The Reciprocal Identities,
    Product Identities: sinθcscθ = 1, cosθsecθ = 1, tanθcotθ = 1
    Quotient Identities: tanθ = sinθ/cosθ, cotθ = cosθ/sinθ
    Pythagorean Identities: cos2θ + sin2θ = 1, 1 + tan2θ= sec2θ, cot2θ + 1 = csc2θ

    3. The attempt at a solution
    38.) cos2x - cos4x ---> (cosx + cos2x)(cosx - cos2x)
    That's as far as I went with this one because I got stumped at this point.

    68.) sec4θ - sec2θ ---> (sec2θ + secθ)(sec2θ - secθ)
    It's the same story with this one. I get stumped after I finish factoring these expressions.
     
  2. jcsd
  3. 38
    cos^2(1-cos^2)----- Pythagorean identity
    cos^2(sin^2)
    the second one is similar
     
  4. Crud, now I feel like an idiot for forgetting about the distributive property. Thanks for the help though!
     
    Last edited: Sep 2, 2011
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