Results 1 to 3 of 3

Math Help - Trigonometric Identities

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    66

    Exclamation Trigonometric Identities

    Given cosec A + cot A = 3, evaluate cosec A - cot A and cos A.

    I was able to evaluate cosec A - cot A:
    cosec^2 A - cot^2 A = 1
    (cosec A - cot A)(cosec A + cot A) = 1
    (cosec A - cot A) x 3 = 1
    Therefore, (cosec A - cot A) = 1/3

    However, I was not able to evaluate cos A.

    The answer should come up to cos A = 4/5.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2010
    From
    Staten Island, NY
    Posts
    451
    Thanks
    2
    Multiply both sides of the equation by \sin A to get 1 + \cos A = 3\sin A.

    Now square both sides to get 1 + 2\cos A + \cos^2 A = 9\sin^2 A = 9(1 - \cos^2 A)

    So 10\cos^2 A + 2\cos A - 8 = 0.

    5\cos^ A + \cos A - 4 = 0

    (5\cos A - 4)(\cos A + 1) = 0

    We get the two solutions \cos A = 4/5, \cos A = -1

    -1 is an extraneous solution since it makes cot A undefined.
    Last edited by DrSteve; November 18th 2010 at 05:06 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    Use what you were given:

    \csc A + \cot A = 3

    1 + \cos A = 3 \sin A .....1

    \csc A - \cot A = \dfrac13

    1 - \cos A = \dfrac{\sin A}{3}

    \sin A = 3 - 3\cos A .........2

    Substitute 2 in 1.

    1 + \cos A = 3(3 - 3\cos A)

    1 + \cos A = 9-9\cos A

    10 \cos A = 8

     \cos A = \dfrac45
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigonometric Identities
    Posted in the Trigonometry Forum
    Replies: 8
    Last Post: November 8th 2011, 09:42 PM
  2. Trigonometric Identities
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: November 4th 2011, 07:06 AM
  3. Trigonometric identities.
    Posted in the Trigonometry Forum
    Replies: 14
    Last Post: November 5th 2010, 09:43 AM
  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 19th 2008, 10:25 PM

Search Tags


/mathhelpforum @mathhelpforum