XPost: comp.os.linux.advocacy
From: crude@sausa.ge
On 2026-01-03 21:17, pothead wrote:
> 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.
Man, how I wish I could still do math.
--
CrudeSausage
John 14:6
Pop_OS!
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