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Math Help - Interesting question regarding the solution to a trigonometric equation

  1. #1
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    Interesting question regarding the solution to a trigonometric equation

    I just saw a very simple question that has generated a lot of interesting discussion within our department.

    Our trigonometry teacher put the question on the board:

    Solve: tan(x) = 1/csc(x)

    Naturally, all the students (and the teacher as well), applied the identity 1/csc(x) = sin(x) and proceeded to say that the solutions were x = (pi)*n, for all integer n.

    However, upon looking at the domain, since csc(x) is undefined for all x = (pi)*n, it would appear that x = (pi)*n is an extraneous root, making the solution the empty set.

    So, is the solution x = (pi)*n or the empty set?

    Thanks in advance!
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  2. #2
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    Crna Gora
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    Re: Interesting question regarding the solution to a trigonometric equation

    empty set...
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