Ask Me Help Desk

Ask Me Help Desk (https://www.askmehelpdesk.com/forum.php)
-   Mathematics (https://www.askmehelpdesk.com/forumdisplay.php?f=199)
-   -   (cot x/1-tan x) +(tan x/1-cot x) = csc x sec x+1 (https://www.askmehelpdesk.com/showthread.php?t=533655)

  • Dec 11, 2010, 04:12 AM
    bellatrix
    (cot x/1-tan x) +(tan x/1-cot x) = csc x sec x+1
    Proving trigonometric identities
  • Dec 11, 2010, 12:57 PM
    galactus



    Transform everything into sin and cos. This is a good idea when solving most any trig identity.









    Note the difference of two cubes in the numerator. Factoring and cancelling leads to:







  • Dec 12, 2010, 05:59 PM
    bellatrix
    Thanks for the answer, but how come the minus sign is missing? Also, how do you solve for the least common denominator in these instances, other than just multiplying it? Thanks!
    [IMG]C:\Documents and Settings\052\Desktop\trig.ident.jpeg[/IMG]
  • Dec 13, 2010, 02:57 AM
    Unknown008

    If you mean the minus sign in the 4th line, this is surely a typing mistake, the line should indeed be



    The LCM in this case will be . You don't multiply again the (sin(x) - cos(x)) because it is present in both denominators, if you see what I mean.
  • Dec 13, 2010, 06:44 PM
    bellatrix
    Comment on Unknown008's post
    but on the left side, the denominator is cos(x)(sin(x) - cos(x)) and on the right side its sin(x)(cos(x) - sin(x))

    is (sin(x) - cos(x)) and (cos(x) - sin(x)) considered the same?
  • Dec 14, 2010, 03:10 AM
    galactus

    No, one is the negative of the other. Thus, the sign change.
    -(sin(x)-cos(x))=cos(x)-sin(x)

  • All times are GMT -7. The time now is 01:15 AM.