Find the value of $\frac{3}{4} \cot ^2 30^{\circ}+\cos ^2 30^{\circ}-3 cosec^2 60^{\circ}+\tan ^2 60^{\circ}$.
Answer & explanation
Correct answer: option 4
\(\frac{3}{4}\). cot²30º + cos²30º - 3 cosec²60º + tan²60º
= \(\frac{3}{4}\) × 3 + \(\frac{3}{4}\) - 3 × \(\frac{4}{3}\) + 3
= \(\frac{9}{4}\) + \(\frac{3}{4}\) - 4 + 3
= \(\frac{12}{4}\) - 4 + 3
= 3 - 4 + 3
= 2