In a triangle ABC, the sides are a = 5, b = 6, and c = 7. What is the value of cos A + cos B + cos C?

In a triangle ABC, if a, b, and c are the lengths of the sides opposite to the angles A, B, and C respectively, then what is sin(A - B)sin(A + B) equal to?

In a triangle ABC, if sin(A) = cos(B) + cos(C), then what is tan(B2) + cot(B2) equal to?