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Solving Trigonometric Identities (A bit Hard)

  1. Dec 2, 2011 #1
    Alright, well I am having a difficult time getting these equations to equal out! I keep hitting trouble and have hit a road block.

    Here is the problem...

    csc(x)+cot(x) = cot(x)csc(x)
    tan(x)+sin(x)

    I am just going to work on the LEFT PART of the equation.

    1 + cos(x)
    sin(x) sin(x)
    ALL OVER
    sin(x) + sin(x)
    cos(x)

    so....
    1 + cos(x) / sin(x) * cos(x) / sin(x) + sin(x)cos(x)

    simplifying the bold leads to...

    1 + cos(x) / sin(x) * cos(x) / sin(x)(1+cos(x))

    I am stuck here, particular getting the common denominator and then simplyfing it out to equal cot(x)csc(x)

    Any help would be appreciated, thanks.
     
  2. jcsd
  3. Dec 2, 2011 #2
    Hello,
    I believe you are on the right track with this solving trigonometric identities.

    (1+Cos(x))/Sin(x) * Cos(x)/(Sin(x) + Sin(x)Cos(x))

    Factor out the Sin(x) on the bottom and cancel the (1+Cos(x)) term (Top and Bottom)

    (1+Cos(x))/Sin(x) * Cos(x)/(Sin(x)*(1+Cos(x))

    thus,

    1/Sin(x) * Cos(x)/Sin(x) = CSC(x)COT(x)
     
  4. Dec 2, 2011 #3
    Thank you so much! I kept going over that problem for about 30 mins; so focused on getting a common denominator that I forget to cross cancel! Ahh, I hate stupid mistakes.

    Thanks,
    - C
     
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