Results 1 to 4 of 4

Math Help - prove identity #3

  1. #1
    Senior Member
    Joined
    Nov 2008
    Posts
    425

    prove identity #3

    prove that (cscx-cotx)^2=(1-cosx)/(1+cosx)

    my steps are as follows:
    LS

    (cscx-cotx)^2
    (1/sinx-1/tanx)^2
    (1/sinx-cosx/sinx)^2
    [(1-cosx)/sinx]^2
    [(1-2cosx-cos^x)/sin^2x]

    now what should I do to get it to equal the other side? I am stuck here
    Last edited by mr fantastic; August 12th 2009 at 04:34 PM. Reason: Changed post title
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member pberardi's Avatar
    Joined
    Dec 2008
    Posts
    85
    Multiply by the one in the form of conjugate of the denominator over the conjugate of the denominator, i.e. 1-cos(x)/1-cos(x). In my book this gives (1-2cos(x) + cos^2(x))/(1-cos^2(x)).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Aug 2008
    Posts
    530

    Reply

    Quote Originally Posted by skeske1234 View Post
    prove that (cscx-cotx)^2=(1-cosx)/(1+cosx)

    my steps are as follows:
    LS

    (cscx-cotx)^2
    (1/sinx-1/tanx)^2
    (1/sinx-cosx/sinx)^2
    [(1-cosx)/sinx]^2 ----------------> You are RIGHT upto here.
    [(1-2cosx-cos^x)/sin^2x] <------------------------------------------> you don't need to do this step.

    now what should I do to get it to equal the other side? I am stuck here
    See after that,

     = \frac{(1- \cos x)^2}{\sin^2 x}

     = \frac{(1- \cos x)^2}{1- \cos^2 x}

     = \frac{(1- \cos x)^2}{(1- \cos x)(1 + \cos x)}

     = \frac{1- \cos x}{1 + \cos x}

    got it ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by skeske1234 View Post
    prove that (cscx-cotx)^2=(1-cosx)/(1+cosx)

    my steps are as follows:
    LS

    (cscx-cotx)^2
    (1/sinx-1/tanx)^2
    (1/sinx-cosx/sinx)^2
    A[(1-cosx)/sinx]^2
    [(1-2cosx-cos^x)/sin^2x]

    now what should I do to get it to equal the other side? I am stuck here
    I'd leave the last line off. From point A which is in red:

    \frac{(1-cos(x))^2}{sin^2(x)} as sin^2(x) = 1-cos^2(x) we can change the denominator

    \frac{(1-cos(x))^2}{1-cos^2(x)}

    Use the difference of two squares on the bottom: 1-cos^2(x) = (1-cos(x))(1+cos(x))

    \frac{(1-cos(x))^2}{(1-cos(x))(1+cos(x))}.
    From here you can cancel 1-cos(x) to give the final answer
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. prove identity help!
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: December 2nd 2010, 10:00 AM
  2. prove the identity
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 7th 2010, 05:03 PM
  3. Prove this identity?
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: April 5th 2010, 05:29 PM
  4. Prove that each of the following is an identity
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 18th 2009, 02:39 PM
  5. Prove the Identity
    Posted in the Trigonometry Forum
    Replies: 10
    Last Post: February 25th 2008, 05:29 PM

Search Tags


/mathhelpforum @mathhelpforum