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Thread: Equating trig identities

  1. #1
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    Question Equating trig identities

    Hi,

    I hope someone can help. It would be great if someone could explain how 2((secx)^4 + 2(secx)^2(tanx)^2) equals -2(cos(2x)-2)(secx)^4

    I know that the expressions are related in some way, I just can't pinpoint what.

    - Olivia
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  2. #2
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    Re: Equating trig identities

    It might be worth converting to sines and cosines...
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    Re: Equating trig identities

    fair point
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    Re: Equating trig identities

    how 2((secx)^4 + 2(secx)^2(tanx)^2) equals -2(cos(2x)-2)(secx)^4
    working on the right side to get the left ...

    $-2(\cos(2x)-2)\sec^4{x}$

    $-2(2\cos^2{x}-1-2)\sec^4{x}$

    $2(3-2\cos^2{x})\sec^4{x}$

    $2(3\sec^4{x} - 2\sec^2{x})$

    $2(\sec^4{x} + 2\sec^4{x} - 2\sec^2{x})$

    $2[\sec^4{x} + 2\sec^2{x}( \sec^2{x} - 1)]$

    $2(\sec^4{x} + 2\sec^2{x}\tan^2{x})$
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