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Suppose that a, b, and c are positive integers such that 24/5=a+(1/(b+(1/c+1))). Find all possible values of a, b, and c.

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).

If a, b, and c are integers and are the sides of a triangle ABC such that b=a(a-c) show that sin(B)/sin(A) is an integer.