$\cos ^{2} \frac{\pi}{24}+\cos ^{2} \frac{19 \pi}{24}+\cos ^{2} \frac{31 \pi}{24}+\cos ^{2} \frac{37 \pi}{24}=?$

Solve:$\begin{array}{l} \cos ^{2} \frac{\pi}{24}+\cos ^{2} \frac{19 \pi}{24}+\cos ^{2} \frac{31 \pi}{24}+\cos ^{2} \frac{37 \pi}{24} \\ =\cos ^{2} \frac{\pi}{24}+\cos ^{2} \frac{19 \pi}{24}+\cos ^{2}\left(\frac{\pi^{\circ}}{2}+\frac{19 \pi}{24}\right) \\ \quad+\cos ^{2}\left(3 \cdot \frac{\pi}{2}+\frac{\pi}{24}\right) \\ =\cos ^{2} \frac{\pi}{24}+\cos ^{2} \frac{19 \pi}{24}+\sin ^{2} \frac{\pi}{24}+\sin ^{2} \frac{19 \pi}{24} \\ =\left(\sin ^{2} \frac{\pi}{24}+\cos ^{2} \frac{\pi}{24}\right)+ \\ \left(\sin ^{2} \frac{19 \pi}{24}+\cos ^{2} \frac{19 \pi}{24}\right) \\ =1+1=2 \text { Ans. } \end{array}$