Results 1 to 5 of 5

Math Help - Trigo identity

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    8

    Trigo identity

    Hello, I need help with this problem
    \frac{\sec{8\theta}-1}{\sec{4\theta}-1} = \frac{\tan{8\theta}}{\tan{2\theta}}

    Thank you.
    Last edited by elitewarr; February 6th 2009 at 10:09 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,688
    Thanks
    447
    Quote Originally Posted by elitewarr View Post
    Hello, I need help with this problem

    \frac{\sec{8\theta}-1}{\sec{4\theta}-1} = \frac{\tan{8\theta}}{\tan{4\theta}}
    as posted, the equation is not an identity ...

    this would be ...

    \frac{\sec^2(8\theta)-1}{\sec^2(4\theta)-1} = \frac{\tan^2(8\theta)}{\tan^2(4\theta)}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2009
    Posts
    8
    My mistake, the tan4 theta should be tan 2 theta. I edited the post.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    \frac{\sec{8\theta}-1}{\sec{4\theta}-1} \:\frac{\tan{2\theta}}{\tan{8\theta}} = \frac{\cos{4\theta}}{\cos{8\theta}} \frac{1-\cos{8\theta}}{1-\cos{4\theta}} \:\frac{\tan{2\theta}}{\tan{8\theta}}

    \frac{\sec{8\theta}-1}{\sec{4\theta}-1} \:\frac{\tan{2\theta}}{\tan{8\theta}} = \frac{\cos{4\theta}}{\cos{8\theta}} \frac{2 \sin^2{4\theta}}{2 \sin^2{2\theta}} \:\frac{\sin{2\theta}}{\sin{8\theta}}\:\frac{\cos{  8\theta}}{\cos{2\theta}}

    \frac{\sec{8\theta}-1}{\sec{4\theta}-1} \:\frac{\tan{2\theta}}{\tan{8\theta}} = \frac{\cos{4\theta} \sin^2{4\theta}}{\sin{2\theta} \sin{8\theta} \cos{2\theta}}

    \frac{\sec{8\theta}-1}{\sec{4\theta}-1} \:\frac{\tan{2\theta}}{\tan{8\theta}} = \frac{\cos{4\theta} \sin^2{4\theta}}{\sin{2\theta}\: 2 \sin{4\theta} \cos{4\theta} \cos{2\theta}}

    \frac{\sec{8\theta}-1}{\sec{4\theta}-1} \:\frac{\tan{2\theta}}{\tan{8\theta}} = \frac{\sin{4\theta}}{2 \sin{2\theta} \cos{2\theta}} = 1
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2009
    Posts
    8
    Wow..Thanks..I thought for more than 1 hour and I still could not find the solution.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigo Identity
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: September 9th 2011, 08:44 PM
  2. Need help with yet another trigo identity
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 13th 2010, 11:19 PM
  3. Complicated Trigo Identity
    Posted in the Trigonometry Forum
    Replies: 9
    Last Post: December 13th 2010, 08:59 PM
  4. derivatives of trigo identity
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 24th 2010, 02:15 AM
  5. trigo: proving an identity
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 31st 2009, 09:12 AM

Search Tags


/mathhelpforum @mathhelpforum