Results 1 to 4 of 4

Math Help - Help with trigonometric identities.

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    39

    Help with trigonometric identities.

    I need some help proving 1/(cscx - cotx) = (1 + cosx)/sinx. I just started dealing with these today and I don't fully comprehend how I am supposed to transform 1/(cscx - cotx) into (1 + cosx)/sinx, so a very detailed explaination would be ideal. Thank you in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Spec's Avatar
    Joined
    Aug 2007
    Posts
    318
    \frac{1}{\csc x-\cot x}=\frac{1}{\frac{1}{\sin x}-\frac{\cos x}{\sin x}}=\frac{\sin x}{1-\cos x}=\frac{\sin x}{1-\cos x}\cdot\frac{1+\cos x}{1+\cos x}=...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Amer's Avatar
    Joined
    May 2009
    From
    Jordan
    Posts
    1,093
    Ok

    you should now that

    cscx = 1/sinx
    cotx = 1/tanx = cosx /sinx
    sin^2x + cos^2x=1

    1/(cscx - cotx ) = 1/( 1/sinx - cosx/sinx )
    = 1/( (1-cosx)/sinx ) = sinx /(1-cosx)
    multiply with 1+cosx/(1+cosx)
    so you have

    sinx (1+cosx)/((1-cosx)(1+cosx))
    sinx(1+cosx)/(1-cos^2)
    sinx(1+cosx)/sin^x.............since sin^2x + cos^2x = 1...sin^2x=1-cos^x
    (1+cosx)/sinx


    Edit: I was late
    Last edited by mr fantastic; May 25th 2009 at 01:12 AM. Reason: Merged posts
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    May 2009
    Posts
    39
    I appreciate the help from the both of you. I have to get used to thinking about how I can finagle these things into what I want.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigonometric Identities
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: June 4th 2011, 10:08 PM
  2. Trigonometric identities
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: December 13th 2009, 06:48 PM
  3. Trigonometric Identities
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: October 6th 2009, 11:02 AM
  4. trigonometric identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 26th 2008, 03:03 PM
  5. trigonometric identities
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: May 8th 2007, 04:41 AM

Search Tags


/mathhelpforum @mathhelpforum