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Math Help - can't seem to figure out how to verify this identity

  1. #1
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    can't seem to figure out how to verify this identity

    sin^4 x + (2 sin^2 x) (cos^2 x) + cos^4 x = 1

    for this one, first, i factored and got:

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

    I don't know if the factoring helped or did anything, but I can't seem to get anything else to get 1.
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  2. #2
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    Quote Originally Posted by tennistudof2009 View Post
    sin^4 x + (2 sin^2 x) (cos^2 x) + cos^4 x = 1

    for this one, first, i factored and got:

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

    I don't know if the factoring helped or did anything, but I can't seem to get anything else to get 1.
    \sin^4{x} + 2\sin^2{x}\cos^2{x} + \cos^4{x} = 1

    (\sin^2{x} + cos^2{x})^2 = 1

    (1)^2 = 1
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  3. #3
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    If you rewrite the problem as
     (\sin^2 x)^2 + 2\sin^2 x \cos^2 x + (\cos^2 x)^2 = 1
    maybe it is a bit clearer.
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  4. #4
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    wow i did some totally unnecessary work...thanks a lot for your help!!!
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  5. #5
    Senior Member pacman's Avatar
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    sin^4 x + (2 sin^2 x) (cos^2 x) + cos^4 x = 1,

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

    1^2 = 1

    1 = 1
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