(a) $\dfrac{\sqrt{1+\cot^2\theta}}{\cot\theta}$
Reason: From the identity $\cosec^2\theta = 1 + \cot^2\theta$, we get $\cosec\theta = \sqrt{1+\cot^2\theta}$. Since $\sec\theta = \dfrac{\cosec\theta}{\cot\theta}$, we get $\sec\theta = \dfrac{\sqrt{1+\cot^2\theta}}{\cot\theta}$.
Use the identity $1 + \cot^2\theta = \cosec^2\theta$, then use $\sec\theta = \tan\theta \cdot \cosec\theta = \dfrac{\cosec\theta}{\cot\theta}$ to express sec θ in terms of cot θ. Options (a) and (c) appear identical in the question; the correct answer is option (a).