Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By Prove It

Math Help - Trigonometric Identities

  1. #1
    Junior Member
    Joined
    Mar 2012
    From
    San Francisco
    Posts
    32

    Question Trigonometric Identities

    Show that:

    sin2(angle) = [tan2(angle)]/[1+tan2(angle)]

    fir all (angles) except odd multiples of pi/2.


    (This is coming straight from my homework)

    -Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,735
    Thanks
    642

    Re: Trigonometric Identities

    Hello, jonathanraxa!

    \text{Show that: }\:\sin^2\!x \:=\:\frac{\tan^2\!x}{1+\tan^2x}

    . . . \text{for all angles except odd multiples of }\tfrac{\pi}{2}

    The right side is:
    . . \frac{\tan^2\!x}{1+\tan^2\!x} \;\;=\;\;\frac{\tan^2\!x}{\sec^2\!x} \;\;=\;\;\frac{\dfrac{\sin^2\!x}{\cos^2\!x}}{ \dfrac{1}{\cos^2\!x}} \;\;=\;\;\frac{\sin^2\!x}{\cos^2\!x}\cdot \frac{\cos^2\!x}{1} \;\;=\;\;\sin^2\!x

    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,547
    Thanks
    1418

    Re: Trigonometric Identities

    Quote Originally Posted by jonathanraxa View Post
    Show that:

    sin2(angle) = [tan2(angle)]/[1+tan2(angle)]

    fir all (angles) except odd multiples of pi/2.


    (This is coming straight from my homework)

    -Thank you!
    First note that \displaystyle \begin{align*} \tan{\theta} \end{align*} is undefined for all odd multiples of \displaystyle \begin{align*} \frac{\pi}{2} \end{align*} (do you know why?) so that means that any combination of \displaystyle \begin{align*} \tan{\theta} \end{align*} will also be undefined at all odd multiples of \displaystyle \begin{align*} \frac{\pi}{2} \end{align*}.

    \displaystyle \begin{align*} \frac{\tan^2{\theta}}{1 + \tan^2{\theta}} &\equiv \frac{\frac{\sin^2{\theta}}{\cos^2{\theta}}}{1 + \frac{\sin^2{\theta}}{\cos^2{\theta}}} \\ &\equiv \frac{\frac{\sin^2{\theta}}{\cos^2{\theta}}}{\frac  {\cos^2{\theta} + \sin^2{\theta}}{\cos^2{\theta}}} \\ &\equiv \frac{\sin^2{\theta}\cos^2{\theta}}{\cos^2{\theta}  \left(\cos^2{\theta} + \sin^2{\theta} \right)} \\ &\equiv \frac{\sin^2{\theta}}{\cos^2{\theta} + \sin^2{\theta}} \\ &\equiv \frac{\sin^2{\theta}}{1} \\ &\equiv \sin^2{\theta} \end{align*}
    Thanks from jonathanraxa
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Mar 2012
    From
    California
    Posts
    44
    Thanks
    6

    Re: Trigonometric Identities

    Trigonometric Identities-sinsin.jpg
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigonometric Identities
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: April 8th 2012, 09:09 AM
  2. [SOLVED] Help with Trigonometric Identities
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: February 16th 2011, 04:47 PM
  3. Trigonometric Identities
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: October 6th 2009, 11:02 AM
  4. Help with trigonometric identities.
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 24th 2009, 02:19 PM
  5. Replies: 3
    Last Post: January 20th 2008, 07:30 PM

Search Tags


/mathhelpforum @mathhelpforum