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Math Help - trig manipulating

  1. #1
    Member i_zz_y_ill's Avatar
    Joined
    Mar 2008
    Posts
    140

    trig manipulating

    Does anyone have any idea how the solution changed sin5\theta+sin\theta into 2sin(3\theta)cos(2\theta) been trying for ages and just can't see it? thanks
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  2. #2
    MHF Contributor Amer's Avatar
    Joined
    May 2009
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    Jordan
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    1,093
    ok this come from

    sin(a+b) = sina cosb + sinb cosa
    sin(a-b) = sina cosb - sinb cosa

    find the sum of two

    sin(a+b) + sin(a-b) = 2 sina cosb

    let a+b = x and a-b =y ..........
    solve this ( find the value of a , b with respect of x .y )

    a = (x+y)/2
    b = (x-y)/2

    now we have
    sinx + siny =2 sin((x+y)/2) cos ((x-y)/2)

    finish
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