The value of tan² 30° - 4 sin² 45° is

1. 1

2. $\dfrac{7}{3}$

3. $-\dfrac{5}{3}$

4. $-\dfrac{11}{3}$

Solving,

$\Rightarrow \text{tan}^2 30° - 4\text{sin}^2 45° = \Big(\dfrac{1}{\sqrt{3}}\Big)^2 - 4 \times \Big(\dfrac{1}{\sqrt{2}}\Big)^2 \\[1em] = \dfrac{1}{3} - 4 \times \dfrac{1}{2} \\[1em] = \dfrac{1}{3} - 2 \\[1em] = \dfrac{1 - 6}{3} \\[1em] = -\dfrac{5}{3}.$

Hence, Option 3 is the correct option.