Results 1 to 4 of 4

Math Help - Proving identity

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    42

    Proving identity

    Prove that 1 - \frac{\cos{x}}{\sec{x}} = \sin^2x
    So I try to prove this by starting from the left hand side of the equation:
    LHS = 1 - \frac{\cos{x}}{\sec{x}}
    = \sin^2{x} + \cos^2{x} - \frac{\frac{\cos{x}}{1}}{\cos{x}}
    = \sin^2{x} + \cos^2{x} - 1
    = \sin^2{x} + \cos^2{x} - (\sin^2{x} + \cos^2{x})
    = 0

    But this is not = \sin^2{x}


    Any pointers? Thank you in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    This line:

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

    cannot become this line:

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

    This:

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

    Becomes this:

        = \sin^2{x} + \cos^2{x} - \left(cos(x)\right)\left(cos(x)\right)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2010
    Posts
    42
    OK, now I can easily solve the problem. Thank you!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    No problem!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proving an identity
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 12th 2009, 10:14 PM
  2. proving an identity
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: September 3rd 2009, 05:37 PM
  3. Proving an identity that's proving to be complex
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: July 21st 2009, 02:30 PM
  4. Proving an identity
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: July 2nd 2009, 10:08 PM
  5. Proving identity #1
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 9th 2009, 03:33 PM

Search Tags


/mathhelpforum @mathhelpforum