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Math Help - could you help me with these problem please ??

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    16

    Red face could you help me with these problem please ??

    My exam is tomorrow could you help me please

    these are my problems
    1\ f(x)=cos^2 (x) is it even or odd ?? show me the solution please
    2\ verify the given identity :
    cos 4x= 1- 8 cos^2 x + 8 cos^4 x

    cos 3x - cos x = 4 cos^3 x - 4 cos x

    sin 3x =3 sin x - 4 sin^3 x

    3\find the exact value :
    sin (2 sin^-1 4\5)

    note sin^-1 = the inverse function of sin


    please help me


    regards ,
    Nora
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  2. #2
    Junior Member
    Joined
    May 2009
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    Zagreb
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    65
    1) cos( -x ) = cos( x ) // cos( x ) is even function

    f( x ) = cos^2( x )

    f( -x ) = cos^2( -x ) = cos( -x )*cos( -x ) = cos( x )*cos( x ) =
    = cos^2( x ) = f( x )
    f( x ) is even function

    2) you can find formulas on internet for this kind of problems

    (hint: cos( 4x ) = cos( 2x + 2x ) , sin( 3x ) = sin( 2x + x ) )

    3)
    sin( 2x ) = 2sin( x )*cos( x )

    cos( x ) = sqrt( 1 - sin^2( x ) )

    sin( 2*sin^-1( 4/5 ) ) = 2*sin( sin^-1( 4/5 ) )*cos( sin^-1( 4/5) ) = 2*( 4/5 )*sqrt( 1 - sin^2( sin^-1( 4/5 ) ) ) =
    = ( 8/5 )*sqrt( 1 - 16/25 ) = ( 8/5 )*sqrt( 9/25 ) = ( 8/5 )*( 3/5 ) = 24/25
    Last edited by josipive; May 15th 2009 at 02:57 AM.
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  3. #3
    Newbie
    Joined
    May 2009
    Posts
    16
    thank you
    Last edited by Nora; May 15th 2009 at 09:27 AM.
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