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| sci.physics | Physical laws, properties, etc. | 178,769 messages |
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| Message 178,581 of 178,769 |
| Physfitfreak to Farley Flud |
| Re: Any Math Heads Out There? |
| 03 Jan 26 20:06:06 |
XPost: comp.os.linux.advocacy From: physfitfreak@gmail.com On 12/24/25 7:30 AM, Farley Flud wrote: > Any math heads out there? > > The following two expressions are equal. That is, substituting any value > of t in the expressions will produce the same value. > > Yet, I cannot reduce one to the other using algebra and the trig identities. > It must be possible but I can't find a way to do it. > > Can you? > > Eternal fame awaits the person who can solve this. > > > Expression 1: > > ⎛ ______________ ⎞ > ⎜ _ ╱ 2 ⎛ 4 2 ⎞ ⎟ > ⎜8 ⋅ ╲╱3 ⋅ cos(t) ⋅ ╲╱ 3 ⋅ cos(t) + 1 ⋅ sin(t) + ⎝27 ⋅ cos(t) + 18 ⋅ cos(t) + 3⎠ ⋅ sin(t)⎟ > ⎜─────────────────── ───────────────────── ───────────────────── ─────────────────── ───────⎟ > ⎜ 4 ⎟ > ⎝ 36 ⋅ cos(t) + 24 ⋅ cos(t) + 4 ⎠ > > > Expression 2: > > ⎛ ______________ ⎞ > ⎜ ╱ 2 ⎛ 2 ⎞ _ ⎟ > ⎜╲╱ 3 ⋅ cos(t) + 1 ⋅ ⎝9 ⋅ cos(t) + 3⎠ ⋅ sin(t) + 8 ⋅ ╲╱3 ⋅ cos(t) ⋅ sin(t)⎟ > ⎜─────────────────── ───────────────────── ───────────────────── ───────────⎟ > ⎜ ______________ ⎟ > ⎜ ╱ 2 ⎛ 2 ⎞ ⎟ > ⎝ ╲╱ 3 ⋅ cos(t) + 1 ⋅ ⎝12 ⋅ cos(t) + 4⎠ ⎠ > > > > > > They're equal. Place the two expressions on either sides of an equal sign. Factor out and get rid of sin(t). Then do the following substitution: a = square root of (3cost^2 +1) Both sides will quickly reduce to the same result in terms of a. --- SoupGate-DOS v1.05 * Origin: you cannot sedate... all the things you hate (1:229/2) |
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