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Some drevative questions

  1. Dec 7, 2009 #1
    Hey guys..
    first, i wanna ask if anyone know a good tutorial or website that can help me with the Treg. deffrentiation, and limits...cause am troubles with that :(
    I got some questions..

    1)

    Prove the Identity Tanx+1/Tanx-1 = Secx-cscx

    I have no clue how to prove sucha a thing..



    2)Evaluate Limx-> Pi/41-Tanx/Sinx-Cosx


    I tried to find any identity to change it's form, but i couldn;t figure anyone out


    And the last one is Deffrentiate Sin2x=2sinxcosx, to devolop the identity of Cos2x


    Y= Sin2x=2sinxcosx
    y'=Cos2x.2 = -2cosxsinx
    y'= Cos2x=-sinxcosx

    But Cos2x should be equal to Cos2x-sin2x ??
     
  2. jcsd
  3. Dec 7, 2009 #2

    Mark44

    Staff: Mentor

    You probably need parentheses on the left side. Otherwise, you have (tanx) +(1/tanx) - 1, and that's probably not what you meant.
    Again, you probably need parentheses. Otherwise, you have (1) - (tanx/sinx) - cosx, and that's probably not what you meant.
    That's differentiate. Also, the word is trigonometry, not tregonometry.
    In the equation above, you have correctly differentiated sin(2x) but not 2sinxcosx. This expression is a product, so you need to use the product rule.
    No, but the derivatative of cos(2x) should be -2sinxcosx = -2sin(2x)
     
  4. Dec 7, 2009 #3
    Am sorry about that Mark

    1)

    Prove the Identity [tex]\frac{Tanx+1}{Tanx - 1}[/tex]=[tex]\frac{Secx+cscx}{Secx-cscx}[/tex]

    2)Evaluate Limx-> Pi/4[tex]\frac{1-Tanx}{Sinx-Cosx}[/tex]

    and thanks for answering number 3 :D
     
  5. Dec 7, 2009 #4

    Mark44

    Staff: Mentor

    For 1, I would change everything to be in terms of sine and/or cosine.
    [tex]LHS~=~ \frac{\frac{sinx}{cosx} + 1}{\frac{sinx}{cosx} - 1}[/tex]

    [tex]RHS~=~\frac{\frac{1}{cosx} + \frac{1}{sinx}}{\frac{1}{cosx} - \frac{1}{sinx}}[/tex]

    Now multiply the left-hand sid (LHS) by 1 in the form of cosx/cosx to simplify it, and multiply the RHS by 1 in the form of (cosx*sinx)/(cosx*sinx). If you end up with LHS = RHS, you will have proved the identity.

    For 2, rewrite the numerator as 1 - (sinx/cosx), and then multiply the whole expression by 1 in the form of cosx/cosx. You should be able to take the limit then.
     
  6. Dec 7, 2009 #5
    For problem 1, ignore the RHS (left-hand side) for now.

    Only look at [tex]\frac{tanx+1}{tanx - 1}[/tex]. What fundamental identities involve tangent?

    [tex]tanx=\frac{sinx}{cosx} and tanx=\frac{1}{cotx}[/tex]

    Any others?

    What about fundamental identities that involve secant (sec) and cosecant (csc)?

    Use some of the fundamental identities and see if you can get the LHS to contain only secants and cosecants.

    Once you are there, you will need a little trick. If you can't figure that part out, come back and ask for more help.
     
  7. Dec 8, 2009 #6
    Thanks for helping me guys... i got number 1 right

    after doing that i got [tex]\frac{Cosz-Sinx}{SinxCosx-Cos^2 x}[/tex]

    and when i take the limit, the dominator still goes to 0
     
  8. Dec 8, 2009 #7
    You have a good start.

    Try L'Hôpital's rule (use only in cases where you have 0/0 or ∞/∞)

    [tex]lim_{n\rightarrow c}\frac{f(x)}{g(x)}=lim_{n\rightarrow c}\frac{f'(x)}{g'(x)}[/tex]

    Then evaluate it and see what you get.
     
  9. Dec 8, 2009 #8

    Mark44

    Staff: Mentor

    Factor the denominator and you'll get some cancellation with the numerator.
     
  10. Dec 8, 2009 #9

    Mark44

    Staff: Mentor

    L'Hopital's Rule is unnecessary for this problem. Also, this is the Precalculus forum, so a calculus technique that requires the knowledge of derivatives is probably inappropriate. OTOH, the OP might have mistakenly posted here.
     
  11. Dec 9, 2009 #10
    I only assumed because of the use of limits, which in my experience are taught in calculus.

    Mspike6: I was able to check the method Mark44 is trying to help you with, so if you want to see a way that takes only a little extra work with no calculus, but ends up much simpler in the end, try to follow his tips.
     
  12. Dec 10, 2009 #11
    Sorry for taking me to long to replay.

    the course am taking is the course right befor Calculas I , It's called Pre-Calculas .

    I did it the way Mark said it worked perfectly.

    Thank you both Mark anf Singular..

    But i would like to ask again...do you, by any chance, know a tutorial or Website that can help me with this Kinda stuff ? Like Trig Limit, Trig Identeties and such .

    Thank you
     
  13. Dec 10, 2009 #12
    Here is a nice http://www.pinkmonkey.com/studyguides/subjects/calc/chap2/c0202701.asp" [Broken].

    The http://en.wikipedia.org/wiki/List_of_trigonometric_identities" [Broken] on trig identities is good, but it probably has more than you will ever need.

    Here is a good condensed http://www.sosmath.com/trig/Trig5/trig5/trig5.html" [Broken].
     
    Last edited by a moderator: May 4, 2017
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