5. Find the value of
$$
\frac{\cos ^{4} 75^{\circ}+\sin ^{4} 75^{\circ}+3 \sin ^{2} 75^{\circ} \cos ^{2} 75^{\circ}}{\cos ^{6} 75^{\circ}+\sin ^{6} 75^{\circ}+4 \sin ^{2} 75^{\circ} \cos ^{2} 75^{\circ}} .
$$
(A) $\frac{\sqrt{2}}{4}$
(B) $\frac{1}{2}$
(C) $\frac{3}{4}$
(D) 1
(E) $\cos 75^{\circ}+\sin 75^{\circ}$
5. Answer:
(D)
$$
\begin{array}{l}
\cos ^{6} x+\sin ^{6} x+4 \sin ^{2} x \cos ^{2} x \\
=\left(\cos ^{2} x+\sin ^{2} x\right)\left(\sin ^{4} x+\cos ^{4} x-\sin ^{2} x \cos ^{2} x\right)+4 \sin ^{2} x \cos ^{2} x \\
=\left(\sin ^{4} x+\cos ^{4} x+3 \sin ^{2} x \cos ^{2} x\right)
\end{array}
$$