Results 1 to 3 of 3

Math Help - [SOLVED] identities of trigonometry

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    2

    [SOLVED] identities of trigonometry

    cosA+cos2A+cos6A+cos7A= 4cosA/2 cos5A/2 cos4A

    (sinA-sinB)(sinA+sinB)= sin(A-B) sin(A+B)

    (sin2A+sin5A-sin3A)/(cosA+1-2sin^2 2A) = 2sinA


    I have no idea how to prove these identities. Could anyone help me saying any idea how to prove? Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    Sum to product formulae

    Hello rolisp

    Welcome to Math Help Forum!
    Quote Originally Posted by rolisp View Post
    cosA+cos2A+cos6A+cos7A= 4cosA/2 cos5A/2 cos4A

    (sinA-sinB)(sinA+sinB)= sin(A-B) sin(A+B)

    (sin2A+sin5A-sin3A)/(cosA+1-2sin^2 2A) = 2sinA


    I have no idea how to prove these identities. Could anyone help me saying any idea how to prove? Thanks
    In each of these questions you need to use the Sum-to-Product formulas (and in #2 and #3, the double-angle formulae) together with basic factorising and simplifying techniques.

    I'll start you off in each case, and leave you to try to complete it.

    1) \cos A +\cos 2A+\cos 6A+\cos 7A
    =2\cos \Big(\frac{3A}{2}\Big)\cos \Big(\frac{A}{2}\Big)+2\cos \Big(\frac{13A}{2}\Big)\cos \Big(\frac{A}{2}\Big)
    Now factorise by taking out a common factor 2\cos \Big(\frac{A}{2}\Big). Then use the same sum-to-product formula again, and you're there.

    2) (\sin A - \sin B)(\sin A + \sin B)
    = 2\cos \Big(\frac{A+B}{2}\Big)\sin\Big(\frac{A-B}{2}\Big)\times 2\sin\Big(\frac{A+B}{2}\Big)\cos\Big(\frac{A-B}{2}\Big)
    Now re-arrange, and use the identity \sin2\theta=2\sin\theta\cos\theta (twice), to write the expression in terms of \sin(A+B) and \sin(A-B).

    3) \frac{\sin2A+\sin5A-\sin3A}{\cos A +1 -2\sin^22A}
    =\frac{2\sin A \cos A +2\cos4A\sin A}{\cos A + \cos 4A}
    Factorise; cancel and you're there.

    Let us know how you get on.

    Grandad
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    2
    I solved these 3 tasks. Thanks for help
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigonometry Identities? Please Help.
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 7th 2010, 09:35 AM
  2. Trigonometry help with identities
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: July 10th 2010, 01:40 PM
  3. Trigonometry Help (Identities)
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: January 6th 2009, 06:46 AM
  4. Trigonometry Identities
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: November 2nd 2008, 06:51 AM
  5. [SOLVED] [SOLVED] help adding and multiplying! trigonometry identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: February 22nd 2007, 04:42 AM

Search Tags


/mathhelpforum @mathhelpforum