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Math Help - [SOLVED] Trig identities - need suggestions

  1. #1
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    [SOLVED] Trig identities - need suggestions

    I understand what to do (for the most part), but need a suggestion or two in how to approach these problems:

    Simplify and reduce:

    (sinx + cscx)(sin^2x + csc^2x-1)

    Factor and reduce:

    sin^4 - cos^4

    The answer to the first one is sin^3 . cos^3 but i have no idea how to solve it.. ive tried it a hundred different ways.

    for the second one, how would I start?
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  2. #2
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    (\sin{x} + \csc{x})(\sin^2{x} + \csc^2{x} - 1) <br />

    multiply it out ...

    \sin^3{x} + \csc{x} - \sin{x} + \sin{x} + \csc^3{x} - \csc{x}

    combine like terms.


    \sin^4{x} - \cos^4{x}

    (\sin^2{x} - \cos^2{x})(\sin^2{x} + \cos^2{x})

    can you finish up from here?
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  3. #3
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    For the first problem:

    (\sin x + \csc x)(\sin^2 x + \csc^2 x - 1)

    \sin^3 x + \sin x \csc^2 x - \sin x + \csc x \sin^2 x + \csc^3 x - \csc x

    \sin^3 x + \csc x - \sin x + \sin x + \csc^3 x - \csc x

    \sin^3 x + \csc^3 x

    Not sure where you would go from there.

    For the second problem:

    \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 - 2 \cos^2 x

    -\cos 2x
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  4. #4
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    Thanks, this helped a lot
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