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Nexus Exotica: Challenge Problem of the Month

  1. Apr 11, 2010 #1
    Problem No. 1

    If 9sinθ - 12cosθ = -13

    then 24sin2θ - 7cos2θ = -X/Y (!!! m & n are relatively prime).

    What is the sum of X & Y?



    Problem No.2

    α and β are real numbers.

    If 2(sinα + cosα)sinβ = 3 - cosβ, evaluate the following:
    3tan2α + 4tan2β



    Apex of Nexus Exotica: The Ultimate Challenge

    Real numbers alpha and beta satisfy the following expressions:
    (α2 + α - 1)(α2 - α + 1) = 2(β3 - 2[tex]\sqrt{5}[/tex] - 1) and (β2 + β - 1)(β2 - β +1) = 2(α3 + 2[tex]\sqrt{5}[/tex] -1).

    Evaluate the following: 4(α2 + 2β3)




    GOOD LUCK!
     
    Last edited: Apr 11, 2010
  2. jcsd
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