Verified answer

sin (25x/2) * cos(x/2)

WE know that

sin(A+B) =sinAcosB+cosAsinB

and sin(A−B) =sinAcosB−cosAsinB

Adding we get

sin(A+B) +sin(A−B) =2sinAcosB

or sinAcosB = ½{sin(A+B) +sin(A−B)}

In sin (25x/2) * cos(x/2) A== 25x/2 and B= x/2

Hence sin (25x/2) * cos(x/2) =½{sin(25x/2+x/2) +sin(25x/2−x/2)}

=½{sin(13x) +sin(12x)}