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Short trig question

  1. Dec 7, 2005 #1

    dnt

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    how is (tan X)(cos X) = (sin X) false?

    tan is sin/cos so when you multiply by cos, you get sin...yet the answer i was given was false? how so?
     
  2. jcsd
  3. Dec 7, 2005 #2

    NateTG

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    Well,
    [tex]\sin \frac{\pi}{2}=1[/tex]
    while
    [tex]\tan \frac{\pi}{2}[/tex]
    is undefined.
     
  4. Dec 8, 2005 #3
    [tex] tan\frac{\pi}{2}[/tex] is undefined because [tex] cos\frac{\pi}{2}[/tex] is zero.
    but that did not answer his question.
    The answer is that [tex](tan x)(cos x)[/tex] is not equal to [tex]sin x[/tex] because when [tex]tan x[/tex] is undefined, the denominator of the trigonometric fraction [tex]\frac{sin x}{cos x}[/tex] is zero and when you have a zero denominator, multiplying by zero in the numerator still results in an undefined result.
     
    Last edited: Dec 8, 2005
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