Results 1 to 2 of 2

Math Help - Trig general Solution

  1. #1
    Member srirahulan's Avatar
    Joined
    Apr 2012
    From
    Srilanka
    Posts
    173

    Arrow Trig general Solution

    Find out the General solution.

    4tanx.tan2x.+3sec^2x=0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,492
    Thanks
    1391

    Re: Trig general Solution

    \displaystyle \begin{align*} 4\tan{x}\tan{2x} + 3\sec^2{x} &= 0 \\ \frac{4\sin{x}\sin{2x}}{\cos{x}\cos{2x}} + \frac{3}{\cos^2{x}} &= 0 \\ \frac{8\sin^2{x}\cos{x}}{\cos{x} \left( 2\cos^2{x} - 1 \right)} + \frac{3}{\cos^2{x}} &= 0 \\ \frac{8\left( 1 - \cos^2{x} \right)\cos{x}}{\cos{x}\left( 2\cos^2{x} - 1 \right)} + \frac{3}{\cos^2{x}} &= 0 \\ \frac{8 \left( 1 - \cos^2{x} \right) \cos^2{x}}{\cos^2{x}\left( 2\cos^2{x} - 1 \right)} + \frac{3\left( 2\cos^2{x} - 1 \right)}{\cos^2{x}\left( 2 \cos^2{x} - 1 \right)} &= 0 \\ \frac{ 8\left( 1 - \cos^2{x} \right)\cos^2{x} + 3\left( 2\cos^2{x} - 1\right) }{ \cos^2{x}\left( 2\cos^2{x} - 1 \right) } &= 0 \\ 8\left(1 - \cos^2{x}\right) \cos^2{x} + 3\left( 2\cos^2{x} - 1 \right) &= 0 \\ 8\cos^2{x}  - 8\cos^4{x} + 6\cos^2{x} - 3 &= 0 \\ 8\cos^4{x} - 14\cos^2{x} + 3 &= 0 \\ 8X^2 - 14X + 3 &= 0 \textrm{ with } X = \cos^2{x} \\ 8X^2 - 2X - 12X + 3 &= 0 \\ 2X(4X - 1) - 3(4X - 1) &= 0 \\ (4X - 1)(2X - 3) &= 0 \end{align*}

    \displaystyle \begin{align*} 4X - 1 = 0 \textrm{ or } 2X - 3 &= 0 \\ X = \frac{1}{4} \textrm{ or } X &= \frac{3}{2} \\ \cos^2{x} = \frac{1}{4} \textrm{ or } \cos^2{x} &= \frac{3}{2} \\ \cos{x} = \pm \frac{1}{2} \textrm{ or } \cos{x} &= \pm \frac{\sqrt{6}}{2} \textrm{ (this is not possible)} \\ x &= \left\{ \frac{\pi}{3}, \frac{2\pi}{3}, \frac{4\pi}{3}, \frac{5\pi}{3}  \right\} + 2\pi n \textrm{ where } n \in \mathbf{Z}  \end{align*}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig general solution
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: August 26th 2012, 07:47 PM
  2. Trig general solution
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: August 24th 2012, 05:46 PM
  3. general solution ,trig?
    Posted in the Calculus Forum
    Replies: 7
    Last Post: June 1st 2009, 06:57 PM
  4. general solution to trig problem
    Posted in the Trigonometry Forum
    Replies: 10
    Last Post: May 18th 2009, 02:28 PM
  5. Trig. Finding the general solution
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 17th 2008, 03:36 PM

Search Tags


/mathhelpforum @mathhelpforum