Results 1 to 8 of 8

Math Help - prove 2

  1. #1
    Member
    Joined
    Nov 2006
    Posts
    152

    prove 2

    tan 20 + 4sin 20 = sqrt 3
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432
    Quote Originally Posted by perash View Post
    tan 20 + 4sin 20 = sqrt 3
    They are not equal.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,842
    Thanks
    320
    Awards
    1
    Quote Originally Posted by perash View Post
    tan 20 + 4sin 20 = sqrt 3
    Quote Originally Posted by DivideBy0 View Post
    They are not equal.
    If they aren't equal they are awfully darned close!

    -Dan
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432
    O geeze it seems i used radians, so sorry
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    The equality is equivalent with
    \sin 20+4\sin 20\cos 20=\sqrt{3}\cos 20\Leftrightarrow
    \Leftrightarrow \sin 20+2\sin 40=\sqrt{3}\cos 20\Leftrightarrow
    \Leftrightarrow \sin 40=\frac{\sqrt{3}}{2}\cos 20-\frac{1}{2}\sin 20\Leftrightarrow
    \Leftrightarrow \sin 40=\cos 30\cos 20-\sin 30\sin 20\Leftrightarrow
    \Leftrightarrow \sin 40=\cos 50\Leftrightarrow
    \Leftrightarrow \sin 40=\sin 40
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,842
    Thanks
    320
    Awards
    1
    Quote Originally Posted by red_dog View Post
    The equality is equivalent with
    \sin 20+4\sin 20\cos 20=\sqrt{3}\cos 20\Leftrightarrow
    \Leftrightarrow \sin 20+2\sin 40=\sqrt{3}\cos 20\Leftrightarrow
    \Leftrightarrow \sin 40=\frac{\sqrt{3}}{2}\cos 20-\frac{1}{2}\sin 20\Leftrightarrow
    \Leftrightarrow \sin 40=\cos 30\cos 20-\sin 30\sin 20\Leftrightarrow
    \Leftrightarrow \sin 40=\cos 50\Leftrightarrow
    \Leftrightarrow \sin 40=\sin 40
    Daaaaaaaaaaaaaang! Do you have a process for figuring these things out or does it just take intuition and experience?

    -Dan
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432
    Awesome stuff red_dog, it looked all the more harder because I've heard that it is not possible to give an exact value for any angle which is not a multiple of 3.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,842
    Thanks
    320
    Awards
    1
    Quote Originally Posted by DivideBy0 View Post
    Awesome stuff red_dog, it looked all the more harder because I've heard that it is not possible to give an exact value for any angle which is not a multiple of 3.
    Funny, that. I can get an exact answer for
    sin(22.5) = sin \left ( \frac{45}{2} \right )
    and 22.5 is not divisible by 3.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove a/b and a/c then a/ (3b-7c)
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 23rd 2010, 05:20 PM
  2. prove,,,
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 1st 2010, 09:02 AM
  3. Prove |w + z| <= |w| +|z|
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 28th 2010, 05:44 AM
  4. Replies: 2
    Last Post: August 28th 2009, 02:59 AM
  5. How to prove that n^2 + n + 2 is even??
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 30th 2008, 01:24 PM

Search Tags


/mathhelpforum @mathhelpforum