Results 1 to 5 of 5

Math Help - trigonometry Prove indentity

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    23

    trigonometry Prove indentity

    [IMG]file:///C:/DOCUME%7E1/Asus/LOCALS%7E1/Temp/moz-screenshot.jpg[/IMG]Cotx - tanx = 2cot2x

    please help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,786
    Thanks
    1570
    Quote Originally Posted by manutd4life View Post
    [IMG]file:///C:/DOCUME%7E1/Asus/LOCALS%7E1/Temp/moz-screenshot.jpg[/IMG]Cotx - tanx = 2cot2x

    please help
    You need to know that

    \cos^2{x} - \sin^2{x} = \cos{2x}

    and

    2\sin{x}\cos{x} = \sin{2x} \implies \sin{x}\cos{x} = \frac{1}{2}\sin{2x}.

    These are proved using the sum formulas (which are proven here)

    Proof of the sum and difference formulas.

    Trigonometric identities

    \cot{x} - \tan{x} = \frac{\cos{x}}{\sin{x}} - \frac{\sin{x}}{\cos{x}}

     = \frac{\cos{x}}{\sin{x}}\times\frac{\cos{x}}{\cos{x  }} - \frac{\sin{x}}{\cos{x}}\times\frac{\sin{x}}{\sin{x  }}

     = \frac{\cos^2{x}}{\sin{x}\cos{x}} - \frac{\sin^2{x}}{\sin{x}\cos{x}}

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

     = \frac{2\cos{2x}}{\sin{2x}}

     = 2\cot{2x}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2008
    Posts
    23
    i have not understand this part clearly
    Quote Originally Posted by Prove It View Post

     = \frac{\cos{x}}{\sin{x}}\times\frac{\cos{x}}{\cos{x  }} - \frac{\sin{x}}{\cos{x}}\times\frac{\sin{x}}{\sin{x  }}

     = \frac{\cos^2{x}}{\sin{x}\cos{x}} - \frac{\sin^2{x}}{\sin{x}\cos{x}}

     = \frac{\cos^2{x} - \sin^2{x}}{\frac{1}{2}\sin{2x}}
    please help how u got this {\frac{1}{2}\sin{2x}}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,786
    Thanks
    1570
    Quote Originally Posted by manutd4life View Post
    i have not understand this part clearly


    please help how u got this {\frac{1}{2}\sin{2x}}
    \frac{\cos^2{x}}{\sin{x}\cos{x}} - \frac{\sin^2{x}}{\sin{x}\cos{x}} = \frac{\cos^2{x}-\sin^2{x}}{\sin{x}\cos{x}} = \frac{\cos{2x}}{\frac{1}{2}\sin{2x}}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2008
    Posts
    23
    Thank you very much
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 26th 2010, 08:42 AM
  2. Prove my mathematics induction, trigonometry
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 13th 2009, 11:21 PM
  3. Trigonometry: Prove the Identity
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: October 27th 2008, 01:50 PM
  4. Trigonometry prove question
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: May 23rd 2006, 03:40 PM
  5. Proving Indentity
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: March 16th 2006, 02:32 PM

Search Tags


/mathhelpforum @mathhelpforum