Results 1 to 3 of 3

Math Help - Identity

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    31

    Identity

    Prove that, sin2x+sin2y=2sin(x+y)cos(x-y).

    help please
    Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    Quote Originally Posted by Hellooo View Post
    Prove that, sin2x+sin2y=2sin(x+y)cos(x-y).

    help please
    Thanks in advance.
    sin(x+y) = sinx*cosy + cosx*siny
    cos(x-y) = cosx*cosy + sinx*siny
    sin(x+y)*cos(x-y) = sinxcosy*cosxcosy + sinxcosy*sinxsiny + cosxsiny*cosxcosy + cosxsiny*sinxsiny
    = sinxcosx*cos^2y + sinycosy*sin^2x + sinycosy*cos^2x + sinxcosx*sin^2y
    So
    2sin(x+y)cos(x-y) = 2[sinxcosx(sin^2y + cos^2y) + sinycosy(sin^2x + sin^2y)]
    = 2sinxcosx + 2sinycosy
    = sin2x + sin2y
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    11
    we can short the solution by using the fact that \sin (a)\cos (b)=\frac{\sin (a+b)+\sin (a-b)}{2}, in our case put (a,b)=(x+y,x-y) and the rest follows trivially.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. identity
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: December 13th 2009, 02:09 PM
  2. identity 2
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: July 27th 2009, 11:26 PM
  3. identity
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: January 21st 2009, 09:40 PM
  4. Sin/Cos Identity
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: September 1st 2008, 04:41 PM
  5. Identity
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 24th 2008, 11:10 AM

Search Tags


/mathhelpforum @mathhelpforum