Let a,b,c denote the three sides of a triangle and A,B,C the corresponding opposite angles. Only..?

one of the expression below has the same value for all triangles. Which one is it?


A) sin A + sin B + sin C;


B) tan A tan B + tan B tan C + tan C tan A;


c) (A + B + C)/(sin A + sin B + sin C);


D) cot A cot B + cot B cot C + cot C cot A;


Kindly explain your answer...

Let a,b,c denote the three sides of a triangle and A,B,C the corresponding opposite angles. Only..?
It's the last one, cot A cot B + cot B cot C + cot C cot A. This follows immediately from setting C = pi - A - B, using the identity cot(pi - x) = - cot x, and then substituting in the formula which gives cot (A + B) as a function of cot A and cot B.