Results 1 to 12 of 12

Math Help - [SOLVED] Proving a Trigonometric Identity

  1. #1
    Newbie mathnewb's Avatar
    Joined
    Apr 2009
    Posts
    16

    Unhappy [SOLVED] Proving a Trigonometric Identity

    my question is this...

    <br /> <br />
\cos x - \cos y=-2  \sin\left (\frac{x + y}{2}\right)\sin\left (\frac{x - y}{2}\right)<br />

    how do you make LHS equal RHS???

    i end up with the RHS equaling

    <br /> <br />
\frac{\cos x \sin y - \sin x \cos y}{2}<br />

    or

    <br /> <br />
\cos x \sin y - \sin x \cos y<br />
without the divided by 2

    please help i need to figure it out by tomorrow...
    Last edited by mr fantastic; April 27th 2009 at 04:26 AM. Reason: Fixed some of the latex
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    ya know that \cos(a+b)=\cos a\cos b-\sin a\sin b, and \cos(a-b)=\cos a\cos b+\sin a\sin b, thus by just subtractin' these we get \cos(a-b)-\cos(a+b)=2\sin a\sin b.

    put x=a-b and y=a+b then solve for (a,b) and you'll get the desired identity.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie mathnewb's Avatar
    Joined
    Apr 2009
    Posts
    16
    where do u subtract the first two identities from????

    and how did u get  2\sin a\sin b ?

    are u working with the LHS or RHS??? I am sorry but i don't understand and i have looked it over again and again.

    could you show me please i find it a little hard to understand what u mean
    Last edited by mathnewb; April 26th 2009 at 09:03 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by mathnewb View Post
    where do u subtract the first two identities from????

    and how did u get  2\sin a\sin b ?

    are u working with the LHS or RHS??? I am sorry but i don't understand and i have looked it over again and again.

    could you show me please i find it a little hard to understand what u mean
    You have been told exactly how to do it.

    You need to go back to post #2 and read it carefully. Try writing it out. Think carefully about what you're writing.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie mathnewb's Avatar
    Joined
    Apr 2009
    Posts
    16
    i understand all steps up to when im supposed to make x=a-b and y=a+b, however, i dont understand what im supposed to solve for (a,b)??

    that part confuses me?!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by mathnewb View Post
    i understand all steps up to when im supposed to make x=a-b and y=a+b, however, i dont understand what im supposed to solve for (a,b)??

    that part confuses me?!
    x = a - b .... (1)

    y = a + b .... (2)

    Solve equations (1) and (2) simultaneously:

    a = \frac{x + y}{2} .... (3)

    b = \frac{y - x}{2} .... (4)


    You know \cos (a - b) - \cos (a + b) = 2 \sin a \sin b.

    Substitute (1) and (2) into the left hand side. Substitute (3) and (4) into the right hand side. You get the identity you were asked to prove.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie mathnewb's Avatar
    Joined
    Apr 2009
    Posts
    16
    could someone please post the full steps and show conclusion where RHS=LHS please!

    i am struggling a lot!!!!
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    no! you try it!

    what you suggest gives me to understand that you want your meal directly into your mouth!
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie mathnewb's Avatar
    Joined
    Apr 2009
    Posts
    16
    i did try it

    this is what i end up with in the end...

    in the beginning i changed x/2 to a and y/2 to b

    this is the last part i end up with

    RHS=(-2cosb^2)+(2cosa^2)

    how can i make this equal cosx-cosy?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by mathnewb View Post
    i did try it

    this is what i end up with in the end...

    in the beginning i changed x/2 to a and y/2 to b

    this is the last part i end up with

    RHS=(-2cosb^2)+(2cosa^2)

    how can i make this equal cosx-cosy?
    I told you how to do it in post #6 (this built on what you had already been told in post #2).

    Although I'm sure it's not the case, your posts do not suggest that you have read or understood anything that has been posted in reply to your problem.

    Please .... clearly state what it is in post #6 that you do not understand and cannot do. Because the complete suggestion has more or less been given to you.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Newbie mathnewb's Avatar
    Joined
    Apr 2009
    Posts
    16

    Unhappy

    ok.....

    when u solve the LHS you get 2sinxsiny....i got that

    the RHS i sub into and get -2sinxsiny

    how do i get rid of negative on RHS???
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Newbie mathnewb's Avatar
    Joined
    Apr 2009
    Posts
    16
    nvm i got it

    thx
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proving a trigonometric identity
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: May 2nd 2010, 10:35 PM
  2. Proving a Trigonometric Identity
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: December 21st 2009, 07:00 AM
  3. proving trigonometric identity
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: May 22nd 2009, 07:46 AM
  4. Proving Trigonometric Identity
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: April 25th 2009, 04:27 PM
  5. trigonometric identity proving need help
    Posted in the Trigonometry Forum
    Replies: 8
    Last Post: December 17th 2008, 06:33 AM

Search Tags


/mathhelpforum @mathhelpforum