Find the exact value of sec (theta) if cot (theta) = -2 and the terminal side of theta lies in quadrant iv. a. sec (theta) = (-sqrt5)/2 b. sec (theta) = (sqrt5)/2 c. sec (theta) = -sqrt5 d. sec (theta) = sqrt5

We know that
sec (theta)=1/cos (theta)

cot (theta) = -2
cot (theta)=cos (theta)/sin (theta)
cos (theta)/sin (theta)=-2> squaring> cos² (theta)/sin² (theta)=4
remember that
sin²(theta)+cos²(theta)=1
sin² (theta)=1-cos² (theta)
substitute
 cos² (theta)/[1-cos² (theta)]=4
cos² (theta)=4*[1-cos² (theta)]> cos² (theta)+4 cos² (theta)=4
5*cos² (theta)=4> cos² (theta)=4/5> cos (theta)=2/√5
cos (theta)=(2√5)/5> is positive  (IV quadrant)
sec (theta)=1/cos (theta)> √5/2

the answer is
sec (theta)=√5/2