Results 1 to 2 of 2

Math Help - prove that a^2sin(A-C)=

  1. #1
    Super Member bigwave's Avatar
    Joined
    Nov 2009
    From
    honolulu
    Posts
    580

    Talking prove that a^2sin(A-C)=

    prove that

    a^2 \sin{\left(B-C\right)} = \left(b^2- c^2\right)\sin{A}

    where
    a,b,c are sides of any triangle
    A,B,C are the corresponding angles
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7
    Quote Originally Posted by bigwave View Post
    prove that

    a^2 \sin{\left(B-C\right)} = \left(b^2- c^2\right)\sin{A}

    where
    a,b,c are sides of any triangle
    A,B,C are the corresponding angles
    \frac{a^2}{b^2-c^2}=\frac{sin^2A}{sin^2B-sin^2C}

    = \frac{sin^2A}{(sinB+sinC)(sinB-sinC)}

    = \frac{sin^2A}{2sin(\frac{B+C}{2})cos(\frac{B-C}{2}).2cos(\frac{B+C}{2})sin(\frac{B-C}{2})}

    = \frac{sin^2A}{2sin(\frac{B+C}{2})cos(\frac{B+C}{2}  ).2sin(\frac{B-C}{2})cos(\frac{B-C}{2})}

    = \frac{sin^2A}{sin(B+C)sin(B-C)}

    = \frac{sin^2A}{sin(\pi-A)sin(B-C)}

    = \frac{sin^2A}{sinAsin(B-C)}

    = \frac{sinA}{sin(B-C)}

    Thus, a^2sin(B-C)=(b^2-c^2)sinA
    Last edited by alexmahone; December 11th 2009 at 01:38 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [2sin^2(x/2) ] / [2sin(x/2)cos(x/2)]
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 13th 2011, 07:15 AM
  2. prove that a^2sin(B-C) =
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 5th 2009, 12:59 AM
  3. prove that sin2x+sin2y=2sin(x+y)cos(x-y)
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: March 29th 2009, 03:15 PM
  4. 2sin^2(x)-sin(x)=3
    Posted in the Trigonometry Forum
    Replies: 9
    Last Post: March 5th 2008, 06:38 PM
  5. int x^2sin^-1(x)
    Posted in the Calculus Forum
    Replies: 4
    Last Post: August 6th 2007, 10:00 PM

Search Tags


/mathhelpforum @mathhelpforum