>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.