The value of $\frac{\tan ^2 30^{\circ}+\sin ^2 90^{\circ}+\cot ^2 60^{\circ}+\sin ^2 30^{\circ} \cos ^2 45^{\circ}}{\sin 60^{\circ} \cos 30^{\circ}-\cos 60^{\circ} \sin 30^{\circ}}$ is:

$\frac{43}{12}$

\(\frac{tan²30º + sin²90º + cot²60º + sin²30º.cos²45º}{sin60º . cos30º - cos60º. sin30º}\)

= \(\frac{1/3 + 1 + 1/3 + 1/4 × 1/2}{√3/2× √3/2 - 1/2×1/2}\)

= \(\frac{5/3  + 1/8}{3/4 - 1/4}\)

= \(\frac{(40+3)/24}{1/2}\)

= \(\frac{43}{12}\)