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Thread: Identities

  1. March 7th 2010, 07:23 PM #1
    purplec16
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    Identities

    tan^4k-sec^4 k=1-sec^2 k
    (tan^2k-sec^2k)(tan^2k+sec^2k)
    (-1)(tan^2k+sec^2k)
    -tan^2k-sec^2k
    What do i do next?
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  2. March 7th 2010, 10:19 PM #2
    Soroban
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    Hello, purplec16!

    There's a typo . . .

    \tan^4\!x-sec^4\!x \;=\;1-{\color{red}2}\sec^2\!x
    Then your work is correct . . .

    (\tan^2\!x-\sec^2\!x)(\tan^2\!x+\sec^2\!x)

    . . \;=\;(-1)(\tan^2\!x+\sec^2\!x)

    . . =\; -\tan^2\!x-\sec^2\!x

    . . . . =\; -(\sec^2x - 1) - \sec^2x

    . . . . =\;-\sec^2x + 1 - \sec^2x

    . . . . =\;1 - 2\sec^2x
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