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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- Dec 10th 2008, 08:05 PMSMA777Trig 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 - Dec 10th 2008, 08:16 PMProve It
Use the identities $\displaystyle \cos{2x} = 2\cos^2{x} - 1$ and $\displaystyle \sin{2x} = 2\sin{x}\cos{x}$.

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

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

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

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

$\displaystyle = \cot{2x}$. - Dec 10th 2008, 08:21 PMSMA777
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! - Dec 10th 2008, 08:25 PMProve It