Evaluate the expression: \(\cot^2 30^\circ - 2\cos^2 60^\circ - \cfrac{3}{4}\sec^2 45^\circ - \sin^2 30^\circ\)

Q.Evaluate the expression: \(\cot^2 30^\circ - 2\cos^2 60^\circ - \cfrac{3}{4}\sec^2 45^\circ - \sin^2 30^\circ\)

\(\cot^2 30^\circ - 2\cos^2 60^\circ - \cfrac{3}{4}\sec^2 45^\circ - \sin^2 30^\circ\) \(= (\sqrt{3})^2 - 2\left(\cfrac{1}{2}\right)^2 - \cfrac{3}{4}(\sqrt{2})^2 - \left(\cfrac{1}{2}\right)^2\) \(= 3 - 2 \times \cfrac{1}{4} - \cfrac{3}{4} \times 2 - \cfrac{1}{4}\) \(= 3 - \cfrac{1}{2} - \cfrac{3}{2} - \cfrac{1}{4}\) \(= \cfrac{12 - 2 - 6 - 1}{4}\) \(= \cfrac{3}{4}\) (Answer)