Let cos x = 1√10 with x in QIV and find: cot2x

Cos x = 1/√10

sin x = √ (1 - 1 / 10) = √9/10 = - 3/√10 (because x is in Q IV)

cot 2 x = cos 2 x/sin 2x = (cos²x - sin²x) / (2 sinx cosx) =

= (1/10 - 3/10) / (2 * (-3/√10) * 1/√10) = ( - 8/10) / (-6/10) = 8/6 = 4/3