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catangent written in short as cot is obtained by 1/tan(x) where x is the angle.Therefor

tan A=opposite/adjacent =10/24 simplify by dividing by 2 gives us =5/12

tan B=opposite/adjacent = 24/10 simplify by dividing by 2 gives us 12/5

To get cot A=1/tan A which gives us 12/5

cot B=1/tan B which gives us 5/12

Hence your correct answer is C , cot A=12/5; cot B=5/12

Hi.I think this addition information may be of importance when solving trigonometric problems.

Assume you have a right angled triangle with sides a,b and c respectively,

sin A = opposite / hypotenuse = a / c

cos A = adjacent / hypotenuse = b / c

tan A = opposite / adjacent = a / b

csc A = hypotenuse / opposite = c / a

sec A = hypotenuse / adjacent = c / b

cot A = adjacent / opposite = b / a

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