Option (A) $\dfrac{3}{4}$
$4\sec\theta = 5 \Rightarrow \sec\theta = \dfrac{5}{4}$, so hypotenuse = 5, adjacent = 4, opposite = $\sqrt{25-16} = 3$.
Therefore, $\cot\theta = \dfrac{\text{adjacent}}{\text{opposite}} = \dfrac{4}{3}$...
Wait — $\cot\theta = \dfrac{4}{3}$, which is option (D).
Answer: (D) $\dfrac{4}{3}$
$4\sec\theta = 5 \Rightarrow \sec\theta = \dfrac{5}{4} \Rightarrow \cos\theta = \dfrac{4}{5}$. Using Pythagoras, $\sin\theta = \dfrac{3}{5}$. Thus $\cot\theta = \dfrac{\cos\theta}{\sin\theta} = \dfrac{4/5}{3/5} = \dfrac{4}{3}$.
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