Find the cosine of both angle A and angle B.

we know that

cos A=adjacent side angle A/hypotenuse
adjacent side angle A=24 units
hypotenuse=26 units

cos A=24/26-----> 12/13

cos B=adjacent side angle B/hypotenuse
adjacent side angle B=10 units
hypotenuse=26 units

cos B=10/26------> 5/13

the answers are
cos A=12/13
cos B=5/13

cot A=adjacent side angle A/opposite side angle A
adjacent side angle A=24 units
opposite side angle A=10 units
cot A=24/10------> cot A=12/5

cot B=adjacent side angle B/opposite side angle B
adjacent side angle B=10 units
opposite side angle B=24 units
cot B=10/24------> cot B=5/12