Answer:
The answer to your question is:
a) cot B = 1/2
b) cos A = 2√5 / 5
c) csc B = √5 / 2
Explanation:
Data
BC = 4
AC = 8
Pythagorean theorem
AB² = AC² + BC²
AB² = 64 + 16
AB² = 80
AB =

Cot B = adjacent side / opposite side = 4/8 = 1/2
cos A = adjacent side / hypotenuse = 8/4√5 = 2

csc B = hypotenuse / opposite side = 4√5 / 8 = √5/2