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quasi
Posts:
11,467
Registered:
7/15/05


Re:    a trig question
Posted:
Mar 22, 2013 2:56 PM


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



