If ABCD is a quadrilateral then cos (A+B/2) + cos (C+D/2) =

answer is zero
For this question we use the relation that cos( 180 - A) = - cos A

For any qudrilateral the sum of the angles is equal to 360 degree.

So, A+ B+ C +D= 360 degree.

=> A+ B = 360 - ( C + D)
divide both side by 2

=> ( A + B)/2 = [360 - (C+ D)]/2

=> (A +B)/2 = 180 - (C+ D)/2

Now take the cos of both the sides:

=> cos (A +B)/2 = cos [180 - (C+ D)/2]

=> cos ( A+ B)/2 = - cos ( C+ D)/2

=> cos ( A+ B)/2 + cos ( C+ D)/2 = 0