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If a and b are distinct real numbers such that a-b and a^2 -b^2 are rational, must a and b be rational?

A function f is called even if f(-x)= f(x) and it is called odd if f(-x)= -f(x). Show that every function f can be written as the sum of an even function and an odd function.

Suppose that an isosceles triangle has sides of length a, a, and b and is such that cos(2A)=sin(B). Show that sin^2(B)=-2sin(A)cos(A)cos(B).