Question 611019
(sec (theta) - cos (theta)) divided by sin (theta). 
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= [sec/sin] - [cos/sin]
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= [1/cos*sin] - cot
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= [2/sin(2x)] - cot(x)
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Note: There are many ways to "simplify"
these trig expressions.  The answer book
can only show one of many possible answers.
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Cheers,
Stan H.