Angle a is in standard position and terminates in quadrant iv. if sec(a) = 4/3 , complete the steps to find cot(a).  use the identity to find the value of ).

We know that
tan²(A)+1 = sec²(A)> tan²(A)= sec²(A)-1
tan²(A)= (4/3)²-1> tan²(A)=16/9-1> 7/9
tan²(A)=7/9
if the angle A is in the IV quadrant
then
tan (A) is negative
therefore
tan (A)=-√(7/9)> tan (A)=-√7/3
so 
cot (A)=1/tan(A)> cot (A)=-3/√7> -(3/7)*√7

the answers are
a) the identity is tan²(A)= sec²(A)-1
b) tan (A)=-√7/3