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Math Help - basic trig

  1. #1
    Junior Member
    Joined
    Jul 2008
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    49

    basic trig

    Factor the expression and use the fundamental identities to simplify the two problems before.

    1) 1-2 sin^2 x + sin^4 x

    2) sec^3 x - sec^2 x - sec x + 1

    Thank you!
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  2. #2
    MHF Contributor
    Joined
    Apr 2008
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    1,092
    1. 1 - 2 \sin^2 x + \sin^4 x

    Substitute u = \sin^2 x to yield:

    1 - 2u + u^2 = (u - 1)^2 = (1 - u)^2

    Back substituting:

    (1 - u)^2 = (1 - \sin^2 x)^2 = (\cos^2 x)^2 = \cos^4 x


    2. \sec^3 x - \sec^2 x - \sec x + 1

    Substitute u = \sec x to yield:

    u^3 - u^2 - u + 1 = (u - 1)^2(u + 1)

    Back substituting:

    (u - 1)^2(u + 1) = (\sec x - 1)^2(\sec x + 1)
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