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Trigonometrical Identities and Simple Equations

  1. May 18, 2007 #1
    Hi there, I am struggling with trigonometrical identities and how to use them effectively. I can work out simpler problems but I cant seem to get my head round slightly bigger ones like this:-

    Simplify:-

    sin^4(x) + 2sin^2(x)cos^2(x) + cos^4(x)

    I 've tried substituting "2sin^2(x)cos^2(x)" with

    sin^2(x) = 1 - cos^2(x)

    and also tried

    cos^2(x) = 1 - sin^2(x)

    but end up going round in circles. Can somebody give me some pointers please!

    Thanks!
     
  2. jcsd
  3. May 18, 2007 #2

    Curious3141

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    sin x = s, cos x = c

    Hint : s^4 + 2s^2c^2 + c^4 = (s^2)(s^2) + (s^2)(c^2) + (c^2)(s^2) + (c^2)(c^2).

    Collect the terms and see what you come up with.
     
  4. May 18, 2007 #3
    Sin^2x + cos^2x =1
     
  5. May 18, 2007 #4

    Kurdt

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    Gold Member

    As Curious has hinted this has been cleverly constructed to be a quadratic in trigonometric functions. It should be quite easy to solve now.
     
  6. May 18, 2007 #5
    Thanks for that! Must remember to factor! That made it easier to solve.
     
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