Results 1 to 6 of 6

Math Help - Trigonometric Identities

  1. #1
    Junior Member casey_k's Avatar
    Joined
    Oct 2008
    From
    Ontario
    Posts
    40

    Exclamation Trigonometric Identities

    I'm having trouble proving this equation.
    Prove:
    (1+ tan x)^2 - sec^2 x = 2 tan x
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,110
    Thanks
    986
    use this Pythagorean identity ...

    1+\tan^2{x} = \sec^2{x}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member casey_k's Avatar
    Joined
    Oct 2008
    From
    Ontario
    Posts
    40

    Exclamation Reply: I'm still a little stuck

    (1+ tan x)^2 - sec^2 x = 2 tan x

    (1 + tan x) (1 + tan x) - sec^2 x

    = 1 + 2 tan x + tan^2 x + 1 - sec^2 x

    = 1 + (2 sin x/cos x) + (sin^2 x/cos^2 x) - (1/cos^2 x)

    = 1 + (2 sin x/cos x) + (sin^2 x - 1/cos^2 x)

    = 1 + (2 sin x/cos x) + (sin^2 x - 1/sin^2 x - 1)

    i cancel out the sin^2 x - 1 and i`m left with

    1 + (2 sin x/cos x) which is close to 2 tan x

    but how do i get rid of the one? any help will be appreciated.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Nov 2008
    Posts
    47
    Last edited by tdschool; November 18th 2008 at 04:48 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,110
    Thanks
    986
    Quote Originally Posted by casey_k View Post
    I'm having trouble proving this equation.
    Prove:
    (1+ tan x)^2 - sec^2 x = 2 tan x
    this may be a less arduous method ...

    (1 + 2\tan{x} + \tan^2{x}) - (1 + \tan^2{x}) =

    1 + 2\tan{x} + \tan^2{x} - 1 - \tan^2{x}) = 2\tan{x}

    you're done.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Nov 2008
    Posts
    47
    My method is more fun, is not?
    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