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Math Help - quick question about reciprocal identity

  1. #1
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    quick question about reciprocal identity

    i am dealing with a function involving sqrt x/ csc x. my textbook shows this problem simplifying to (sqrt x sin x). did they use the reciprocal identity? my trig textbook states that sin x= 1/ csc x. is it true to say then that (1)sin x= 1/ csc x? or in this case, sqrt x sin x= sqrt x/ csc x?
    Last edited by jn23; January 29th 2013 at 01:14 PM.
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  2. #2
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    Re: quick question about reciprocal identity

    By definition, \csc x = 1 / \sin x, so \csc x is undefined for x=\pi k, k\in\mathbb{Z}. Therefore, \csc x\ne0 for all x and \sin x = 1 / \csc x for x\ne\pi k, k\in\mathbb{Z}.
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