1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simplifying Trigonometric Equations

  1. Sep 2, 2011 #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
    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. Sep 2, 2011 #2
    cos^2(1-cos^2)----- Pythagorean identity
    the second one is similar
  4. Sep 2, 2011 #3
    Crud, now I feel like an idiot for forgetting about the distributive property. Thanks for the help though!
    Last edited: Sep 2, 2011
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Simplifying Trigonometric Equations