XPost: comp.os.linux.advocacy
From: pothead@snakebite.com
On 2026-01-04, Physfitfreak wrote:
> 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.
Correct.
Factor.
Simplify the fraction
Factor once more.
Simplify the fraction again.
Both expressions are equal.
Easy peasy.
--
pothead
“Liberals seem to assume that, if you don’t believe in their particular
political solutions, then you don’t really care about
the people that they claim to want to help.”
― Thomas Sowell
--- SoupGate-DOS v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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