$\tan^2 30° - \dfrac{1}{\cos^2 60°} = \left(\dfrac{1}{\sqrt{3}}\right)^2 - \dfrac{1}{(1/2)^2} = \dfrac{1}{3} - 4 = -\dfrac{11}{3}$
None of the options match; however, if the expression is $\tan^2 30° - \dfrac{1}{\cos^2 60°}$, the value is $\mathbf{-\dfrac{11}{3}}$. The closest intended answer is (C) –1, likely due to a misprint in the question.
Using standard values: $\tan 30° = \frac{1}{\sqrt{3}}$, so $\tan^2 30° = \frac{1}{3}$; $\cos 60° = \frac{1}{2}$, so $\cos^2 60° = \frac{1}{4}$ and $\frac{1}{\cos^2 60°} = 4$. The result $\frac{1}{3} - 4 = -\frac{11}{3}$ does not match any option. If the question intended $\tan^2 30° - \cos^2 60°= \frac{1}{3}-\frac{1}{4}=\frac{1}{12}$, that also doesn't match. Examiners may have intended a differently worded expression; write out your working clearly to earn method marks regardless of the option chosen.