question_answer

The sides of a \[\Delta \,ABC\]are in AP, if the angles A and C are the greatest and the smallest angles respectively, then \[4\,\,\left( 1-cos\,A \right)\left( 1cos\,C \right)\] is equal to _______.

A)  \[{{\cos }^{2}}\frac{A+C}{2}\]                      

B)  \[2{{\cos }^{2}}\frac{A+C}{2}\]

C)  \[4{{\cos }^{2}}\frac{A+C}{2}\]                    

D)  \[8{{\cos }^{2}}\frac{A+C}{2}\]

E)  None of these