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Math Help - Trig Proof/Verification : cot 2x = (1+cos4x)/sin4x

  1. #1
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    Trig Proof/Verification : cot 2x = (1+cos4x)/sin4x

    Sorry, another one.

    If you could just explain how to split up the cos4x and sin4x, that would be helpful as well!

    Thank you:

    cot 2x = (1+cos4x)/sin4x
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  2. #2
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    Quote Originally Posted by SMA777 View Post
    Sorry, another one.

    If you could just explain how to split up the cos4x and sin4x, that would be helpful as well!

    Thank you:

    cot 2x = (1+cos4x)/sin4x
    Use the identities \cos{2x} = 2\cos^2{x} - 1 and \sin{2x} = 2\sin{x}\cos{x}.


    \frac{1 + \cos{4x}}{\sin{4x}} = \frac{1 + \cos{2\times 2x}}{\sin{2\times 2x}}

     = \frac{1 + 2\cos^2{2x} - 1}{2\sin{2x}\cos{2x}}

     = \frac{2\cos^2{2x}}{2\sin{2x}\cos{2x}}

     = \frac{\cos{2x}}{\sin{2x}}

     = \cot{2x}.
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    In your very first step, is it cos(2) * 2x or cos(2*2x), because the latter makes more sense, but in that case the step after that does not ...

    Oh wait! I got it - becuase it's 2x the x in the Double Angle Formula is TWO x as well. Ah. Thank you!
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  4. #4
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    Quote Originally Posted by SMA777 View Post
    In your very first step, is it cos(2) * 2x or cos(2*2x), because the latter makes more sense, but in that case the step after that does not ...

    Oh wait! I got it - becuase it's 2x the x in the Double Angle Formula is TWO x as well. Ah. Thank you!
    Yes it's \cos{(2\times 2x)}.
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