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Topic: ----- ---- ----- a trig question
Replies: 1   Last Post: Mar 22, 2013 2:56 PM

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quasi

Posts: 10,232
Registered: 7/15/05
Re: ----- ---- ----- a trig question
Posted: Mar 22, 2013 2:56 PM
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Deep wrote:

>Consider the following two trig.equations.
>
>s = (sin 5D)^(2/5) (1)
>
>c = (cos 5D)^(2/5) (2)
>
>where s and c are real numbers such that 0<c<1 and 0<s<1;
>0<D<pi/2
>
>Statement: Both s and c cannot be rational.


Both s and c can be positive rational (separately).

But they can't both be positive rational (simultaneously).

Suppose s and c are both positive rationals.

Then s^5 + c^5 = sin^2(5D) + cos^2(5D) = 1.

But s^5 + c^5 = 1 with s,c positive rational contradicts
FLT for n = 5.

Many times you've posted questions nearly identical to the
one above. Evidently you've learned nothing from the answers
given.

You're chasing your own tail.

quasi



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