We have cot x= 1/5. We need the value of (cos x)^2

(sin x)^2 + (cos x)^2 = 1

divide all terms by (sin x)^2

=> 1 + (cot x)^2 = 1/(sin x)^2

substitute cot x = 1/5

=> 1 + (1/5)^2 = 1/(sin x)^2

=> 1/(sin x)^2 = 1 + 1/25

=> 1/(sin x)^2 = 26/25

=> (sin x)^2 = 25/26

=> 1 - (cos x)^2 = (25/26)

=> (cos x)^2 = (1 - 25/26)

=> (cos x)^2 = (1/26)

**The value of (cos x)^2 = 1/26**

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