If sin θ = $\Big(\dfrac{1}{2}\Big)$, then the value of $\Big(\dfrac{1}{5} \cot^2\theta + \dfrac{1}{5}\Big)$ is:

1. $\Big(\dfrac{1}{5}\Big)$

2. $\Big(\dfrac{4}{5}\Big)$

3. $\Big(\dfrac{1}{125}\Big)$

4. 25

Solving,

$\Rightarrow \Big(\dfrac{1}{5} \cot^2\theta + \dfrac{1}{5}\Big) \\[1em] \Rightarrow \dfrac{1}{5} \Big(\cot^2\theta + 1 \Big) \\[1em] \Rightarrow \dfrac{1}{5} (\cosec^2 \theta).$

We know that,

$\cosec \theta = \dfrac{1}{\sin \theta } \\[1em] \Rightarrow \cosec \theta = \dfrac{1}{\dfrac{1}{2}} = 2\\[1em] \Rightarrow \cosec^2 \theta = 2^2 = 4 \\[1em] \Rightarrow \dfrac{1}{5}\cosec^2 \theta \\[1em] \Rightarrow \dfrac{1}{5}(4) \\[1em] \Rightarrow \dfrac{4}{5}.$

Hence, option 2 is the correct option.