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Math Help - Trig Problem

  1. #1
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    Trig Problem

    [sec(theta)*csc(theta)=2csc(theta)

    I have been working on this problem forever, and I finally decided to seek help. My first thought upon seeing this problem was to divide both sides by csc(theta) leaving the equation as sec(theta)=csc(theta), but that isn't the right answer. For some reason the answer seems obvious, but I can't find it. Can someone help me please?

    I really want to work it out myself, but can someone just nudge me in the right direction?
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  2. #2
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    \sec{t} \csc{t} = 2\csc{t}

    0 = 2\csc{t} - \sec{t}\csc{t}

    0 = \csc{t}(2 - \sec{t})

    \csc{t} is never 0, so \sec{t} = 2

    can you finish?
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  3. #3
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    Thank you so much!! These problems have always been a pain for me.

    One more question. Is the reason csc(theta) is never equal to zero because it would be undefined?
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  4. #4
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    \csc{t} = \frac{1}{\sin{t}}

    will any value of \sin{t} (which are between -1 and 1) ever make the right side of the above equation equal 0?
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  5. #5
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    It would depend on if you are talking about an angle (theta) or an unknown value (such as t) right?

    Since csc=r/y, with r=1 on the unit circle, y would equal 0 at 2pi and/or 0.

    I think I'm starting to confuse myself.
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  6. #6
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    you're making this too hard ... it doesn't matter what the angle theta is.

    bottom line is that csct = 1/sint, and 1 divided by anything between -1 and 1 can never equal 0.
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  7. #7
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    I tend to do that.

    Thank you for helping.
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