Cos \(\theta\) = \(\frac{12}{13}\) x\(^2\) + 12\(^2\) = 13\(^2\) x\(^2\) = 169- 144 = 25 x = \(\sqrt{25}\) = 5 Hence, tan\(\theta\) = \(\frac{5}{12}\) and cos\(\theta\) = \(\frac{12}{13}\) If cot\(^2\)\(\theta\) = 1 + \(\frac{1}{tan^2\theta}\) = 1 + \(\frac{1}{\frac{(5)^2}{12^2}}\) = 1 + \(\frac{1}{\frac{25}{144}}\) = 1 + \(\frac{144}{25}\) = \(\frac{25 + 144}{25}\) = \(\frac{169}{25}\)