An angle of a right triangle has a cotangent value of 5/12. complete the statements using the given information and the diagram shown on the right. a = b = c =

The complete question in the attached figure

Part 1) find sec (theta)

we know that
sec (theta)=1/ cos (theta)
cos (theta)=adjacent side angle theta/hypotenuse
adjacent side angle theta=5
hypotenuse=13
so
cos (theta)=5/13
sec (theta)=1/(5/13)-------> sec (theta)=13/5

the answer Part 1) is
sec (theta) = 13/5

Part 2)simplify sec(theta)*cos (theta)
sec (theta)=13/5
cos (theta)=5/13
so
sec(theta)*cos (theta)=(13/5)*(5/13)----> 1

the answer part 2) is 1

Part 3)simplify cot(theta)/cos(theta)
cot (theta)=5/12
cos (theta)=5/13
so
cot(theta)/cos(theta)=(5/12)/(5/13)----> 13/12

we know that
sin (theta)=opposite angle theta/hypotenuse
opposite side angle theta=12
hypotenuse=13
sin (theta)=12/13
csc (theta)=1/sin (theta)------> csc (theta)=1/(12/13)----> csc (theta)=13/12
therefore
cot(theta)/cos(theta)=csc (theta)

the answer Part 3) is 
csc (theta)

Part 4)simplify cot(theta)*sin(theta)
cot (theta)=5/12
sin (theta)=12/13
so
 cot(theta)*sin(theta)=(5/12)*(12/13)----> 5/13
cos (theta) =5/13
therefore
cot(theta)*sin(theta)=cos (theta)

the answer part 4) is
cos (theta)