if cos x is positive and sin x is negative so the angle x belong to the IV quadrant
cos x=5/13 we know that sin²x+cos²x=1-------> sin²x=1-cos²x------> 1-(5/13)²---> 144/169 sin x=√(144/169)-------> sin x=12/13 but remember that x is on the IV quadrant so sin x=-12/13
Part A) <span>cos (x/2) cos (x/2)=(+/-)</span>√[(1+cos x)/2] cos (x/2)=(+/-)√[(1+5/13)/2] cos (x/2)=(+/-)√[(18/13)/2] cos (x/2)=(+/-)√[36/13] cos (x/2)=(+/-)6/√13-------> cos (x/2)=(+/-)6√13/13 the angle (x/2) belong to the II quadrant so cos (x/2)=-6√√13/13
the answer Part A) is cos (x/2)=-6√√13/13
Part B) sin (2x) sin (2x)=2*sin x* cos x------> 2*[-12/13]*[5/13]----> -120/169
