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Trigo Identity applications

  1. Sep 1, 2008 #1
    1. The problem statement, all variables and given/known data
    If [tex]\frac{(cos x)^{4}}{(cos y)^{2}}+\frac{(sin x)^{4}}{(sin y)^{2}}=1 [/tex] prove that

    [tex]\frac{(cos y)^{4}}{(cos x)^{2}}+\frac{(sin y)^{4}}{(sin x)^{2}}=1 [/tex]

    3. The attempt at a solution
    [tex](cos x)^{4} (sin y)^{2}+(sin x)^{4} (cos y)^{2}=(sin y)^{2}-(sin y)^{4}[/tex]

    On simplification:
    [tex]\frac{(sin y)^{4}}{(sin x)^{2}}=(sin y)^{2}+ (cos x)^{2} (sin y)^2 - (sin x)^{2}(cos y)^{2}[/tex]

    Similarly for cos
    [tex]\frac{(cos y)^{4}}{(cos x)^{2}}=(cos y)^{2}+ (cos y)^{2} (sin x)^2 - (cos x)^{2}(sin y)^{2}[/tex]

    Adding the above gives the result.

    But is their any simpler way?
  2. jcsd
  3. Sep 1, 2008 #2


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    Science Advisor
    Homework Helper

    Am I missing something, because both your identities are identical?!
  4. Sep 2, 2008 #3
    There is nothing missing. Please check it out once again, they are indeed different.
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