Let ABC be a right triangle such that C = pi/2, 0<A<pi/2 Sides a, b are integers and c^2 is an integer but c is not an integer. This implies both Sin A and Cos A are irrational.
Conjecture: Both (sin 5A)^(2/5) and (cos 5A)^(2/5) can not be rational. Any helpful comment about the conjecture will be appreciated. If the conjecture is valid can it also be extended for sin 7A and cos 7A?