Results 1 to 4 of 4

Math Help - Trigonometric Identities

  1. #1
    Junior Member
    Joined
    Apr 2008
    Posts
    30

    Trigonometric Identities

    Could someone PLEASE help me with these!
    1. Verify the identity: (sinx-2+1/sinx)/(sinx-1/sinx)=sinx-1/sinx+1
    2.Verify the identity: (1/1-cosx)-(cosx/1+cosx)=2csc(squared)x-1
    3.Verify the identity: 2cos4xsin2x=2sin3xcos3x-2cosxsinx
    Last edited by kelsey3; April 6th 2008 at 03:00 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641

    Ok

    here is what you have \frac{sin(x)-2+\frac{1}{sin(x)}}{sin(x)-\frac{1}{sin(x)}}..multiply top and bottom by sin(x) to get \frac{sin(x)^2-2sin(x)+1}{sin(x)^2-1} which simplifies to \frac{(sin(x)-1)^2}{(sin(x)-1)(sin(x)+1)}..and by cancelling the common factor of sin(x)-1 you get what you want
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jan 2008
    From
    UK
    Posts
    484
    Thanks
    66
    \frac{sinx-2+1/sinx}{sinx-1/sinx}=\frac{sinx-1}{sinx+1}

    Working on the LHS

    Multiply top and bottom by sinx and then factorise.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641

    For the secodn one

    \frac{1}{1-cos(x)}-\frac{cos(x)}{1+cos(x)} which then by combining the fraction gives you \frac{1+cos(x)-cos(x)+cos(x)^2}{sin(x)^2}...the top simplifies to \frac{2-sin(x)^2}{sin(x)^2} by manipulating the pythagorean identity..now seperating that gives what you wnat
    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, 11:08 PM
  2. Trigonometric identities
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: December 13th 2009, 07:48 PM
  3. Trigonometric Identities
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: October 6th 2009, 12:02 PM
  4. trigonometric identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 26th 2008, 04:03 PM
  5. trigonometric identities
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: May 8th 2007, 05:41 AM

Search Tags


/mathhelpforum @mathhelpforum