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Factoring trigonometric equation

  1. Nov 21, 2006 #1
    Hi,

    I'm having trouble understanding how my math book factored the following equation.

    [(cos(t)sin(t) - (1 + sin(t))cos(t)) / (cos(t)cos(t) - (1 + sin(t))sin(t))]

    to get

    [(cos(t)(1+2sin(t))) / ((1 + sin(t)) (1 - 2sin(t)))]

    I get the numerator but I dont understand what happend to the cosine in the denominator..

    Any suggestions?

    Thanks
     
  2. jcsd
  3. Nov 21, 2006 #2

    Hurkyl

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    Staff Emeritus
    Science Advisor
    Gold Member

    I don't believe those are equal. For example, if you plug in t=0, the first expression is equal to -1, and the second is +1. Presumably it's just a typo.

    Anyways, this is why you studied trig identities in precalc. :smile: Pretend you were given the following problem.


    Prove the identity:
    (cos t)(cos t) - (1 + sin t)(sin t) = (1 + sin t)(1 - 2 sin t)​
     
    Last edited: Nov 21, 2006
  4. Nov 21, 2006 #3
    oh right

    cos^2(x) + sin^2(x) = 1

    thanks!
     
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