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    just wanna check a trig question

    sinx+sin3x=sin2x

    just give us a simple answer (only 1 needed)

    i get 60 but can people show how they did this???
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    If you only need one answer, then how about x = 0?!

    (cos(x) + i sin(x))^3 = cos(3x) + i sin(3x)
    so, taking imaginary part, 3sin(x)cos^2(x) - sin^3(x) = sin(3x).

    So sin(x) + sin(3x) = sin(2x) is equivalent to

    sin(x) (1 - 2cos(x) + 3cos^2(x) - sin^2(x)) = 0
    <=> sin(x) (-2cos(x) + 4cos^2(x)) = 0
    <=> 2 sin(x) cos(x) (-1 + 2cos(x)) = 0
    <=> sin(x) = 0 or cos(x) = 0 or cos(x) = 1/2.
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    (Original post by lgs98jonee)
    just wanna check a trig question

    sinx+sin3x=sin2x

    just give us a simple answer (only 1 needed)

    i get 60 but can people show how they did this???
    sinx+sin3x-sin2x=0 =>2sin(2x)cos(x)-sin(2x)=0
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    sinx + sin3x = sin2x
    => 2sin2xcosx = sin2x
    => sin2x(2cosx - 1) =0
    etc
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    (Original post by Jonny W)
    If you only need one answer, then how about x = 0?!

    (cos(x) + i sin(x))^3 = cos(3x) + i sin(3x)
    so, taking imaginary part, 3sin(x)cos^2(x) - sin^3(x) = sin(3x).

    So sin(x) + sin(3x) = sin(2x) is equivalent to

    sin(x) (1 - 2cos(x) + 3cos^2(x) - sin^2(x)) = 0
    <=> sin(x) (-2cos(x) + 4cos^2(x)) = 0
    <=> 2 sin(x) cos(x) (-1 + 2cos(x)) = 0
    <=> sin(x) = 0 or cos(x) = 0 or cos(x) = 1/2.
    i think complex numbers is a bit beyond this!
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    expand to

    sin x +sin2xcosx + cos2xsinx = 2cosxsinx
    sin x + 2sinxcosxcosx + (2(cos^2)x -1)sin x = 2cosxsinx

    sin x=0 is a solution

    and

    1 + 2(cos^2)x + 2(cos^2)x -1) = 2cos x

    so

    4(cos^2)x = 2cos x

    so cos x = 0 is a solution and

    cos x = 0.5 is a solution.
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    (Original post by Jonny W)
    How did you prove sin(x) + sin(3x) = 2sin(2x)cos(x)?
    Using the sum-product formula for sin A + sin B?
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    (Original post by Jonny W)
    How did you prove sin(x) + sin(3x) = 2sin(2x)cos(x)?
    sinA+sinB=2sin((A+B)/2)cos((A-B)/2). C'mon u should know that!
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    dont bother memorising it, its in the formula book lol
 
 
 
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