Results 1 to 3 of 3

Math Help - Trig Identities

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

    Arrow Trig Identities

    (hi) I'm having trouble with the longer problems.

    (sin x + cos x)/(sin x-cos x) = secē x + 2 tan x/ secē - 2 tan x
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,678
    Thanks
    611
    Hello, casey_k!

    \frac{\sin x + \cos x}{\sin x-\cos x} \:=\: \frac{\sec^2\!x + 2\tan x}{\sec^2\!x- 2\tan x} . . . . This is not an identity.
    Is the first fraction squared? . \left(\frac{\sin x + \cos x}{\sin x - \cos x}\right)^2 \;=\;\frac{\sec^2\!x + 2\tan x}{\sec^2\!x - 2\tan x}


    The left side is: . \frac{\overbrace{\sin^2\!x + \cos^2\!x}^{\text{This is 1}} + \:2\sin x\cos x}{\underbrace{\sin^2\!x + \cos^2\!x}_{\text{This is 1}} - \:2\sin x\cos x} \;=\; \frac{1 + 2\sin x\cos x}{1 - 2\sin x\cos x}

    Divide top and bottom by \cos^2\!x\!:\;\;\frac{\dfrac{1}{\cos^2\!x} + \dfrac{2\sin x\cos x}{\cos^2\!x}} {\dfrac{1}{\cos^2\!x} - \dfrac{2\sin x\cos x}{\cos^2\!x}}

    . . . . =\;\;\frac{\sec^2\!x + 2\,\dfrac{\sin x}{\cos x}}{\sec^2\!x - 2\,\dfrac{\sin x}{\cos x}} \;\;=\;\;\frac{\sec^2\!x + 2\tan x}{\sec^2\!x - 2\tan x}<br /> <br />


    Follow Math Help Forum on Facebook and Google+

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

    Reply: Not Identity

    Yes, the left side is squared. I forgot to add the square.

    Thank you so much for your help!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig Identities
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 3rd 2009, 06:44 AM
  2. Trig identities
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: June 22nd 2009, 06:58 AM
  3. Trig Identities
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 9th 2008, 04:35 PM
  4. Trig Identities Help!!!!
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 14th 2008, 11:47 AM
  5. Trig Identities
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: November 12th 2006, 07:59 PM

Search Tags


/mathhelpforum @mathhelpforum