Find the value of $\frac{8 \sin 30^{\circ} \sin ^2 60^{\circ}-4 \sin 90^{\circ}-\sec ^2 45^{\circ}}{\tan ^2 45^{\circ}-\cot ^2 30^{\circ}}$
Answer & explanation
Correct answer: option 4
$\frac{8 \sin 30^{\circ} \sin ^2 60^{\circ}-4 \sin 90^{\circ}-\sec ^2 45^{\circ}}{\tan ^2 45^{\circ}-\cot ^2 30^{\circ}}$
= \(\frac{ 8 × 1/2 × 3/4 - 4 - 2 }{ 1 - 3}\)
= \(\frac{3 - 4 - 2 }{ -2 }\)
= \(\frac{3 }{ 2 }\)