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Math Help - Proving Trigonometric Identities

  1. #1
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    Proving Trigonometric Identities

    Hey i need some help

    sin^4 (X) - cos^4 (X) = 1 - 2cos^2(X)
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  2. #2
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    Quote Originally Posted by oneway1225 View Post
    Hey i need some help

    sin^4 (X) - cos^4 X = 1 - 2cos^2(X)
    Note that the left hand side is a difference of two squares: (\sin^2 x - \cos^2 x) (\sin^2 x + \cos^2 x).
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  3. #3
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    Hello,

    Here is a way of solving this:

    sin^4(x)-cos^4(x)=[sin^2(x)-cos^2(x)][sin^2(x)+cos^2(x)] =sin^2(x)-cos^2(x)=1-cos^2(x)-cos^2(x)=1-2cos^2(x)<br />

    Have a nice day,
    Hush_Hush.
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  4. #4
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    Quote Originally Posted by Hush_Hush View Post
    Hello,

    Here is a way of solving this:

    sin^4(x)-cos^4(x)=[sin^2(x)-cos^2(x)][sin^2(x)+cos^2(x)] =sin^2(x)-cos^2(x)=1-cos^2(x)-cos^2(x)=1-2cos^2(x)<br />

    Have a nice day,
    Hush_Hush.

    how did you go from [sin^2(x)-cos^2(x)][sin^2(x)+cos^2(x)] to sin^2(x)-cos^2(x)
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  5. #5
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    Quote Originally Posted by oneway1225 View Post
    how did you go from [sin^2(x)-cos^2(x)][sin^2(x)+cos^2(x)] to sin^2(x)-cos^2(x)
    What is always the value of \sin^2(x)\, +\, \cos^2(x)?

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  6. #6
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