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Math Help - Simplify Trig Identities

  1. #1
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    Simplify Trig Identities

    Thank you very much...i got mono and now this stuff is killing me

    Simplify the following expressions:

    1. (cscX - 1)
    secX

    2. tanX - secX
    tanX + secX

    thank you so much for you help
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  2. #2
    Super Member
    Joined
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    Quote Originally Posted by krizzle13 View Post
    Thank you very much...i got mono and now this stuff is killing me

    Simplify the following expressions:

    1. (cscX - 1)
    secX

    2. tanX - secX
    tanX + secX

    thank you so much for you help
    1. \frac{\csc{x}-1}{\sec{x}} = \frac{\frac{1}{\sin{x}}-1}{\frac{1}{\cos{x}}}

    Multiply by \frac{\sin{x}\cos{x}}{\sin{x}\cos{x}} to get:

    \frac{\cos{x}-\sin{x}\cos{x}}{\sin{x}} = \frac{\cos{x}}{\sin{x}}-\cos{x} = \cot{x} - \cos{x}

    2. Multiplying by \frac{\tan{x}-\sec{x}}{\tan{x}-\sec{x}} does the trick. Recall that \tan^2{x} + 1 = \sec^2{x} \implies \tan^2{x}-\sec^2{x}=-1

    After multiplying, you should get:
    \frac{(\tan{x}-\sec{x})^2}{-1} = -(\tan{x}-\sec{x})^2
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  3. #3
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    thank you so much...makes sense now
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