cos 45° cos 30° + sin 45° sin 30°

On substituting the values of various T-ratios, we get:
 cos 45o cos 30o + sin 45o  sin 30o 

$=\left(\frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}} \times \frac{1}{2}\right)=\left(\frac{\sqrt{3}}{2 \sqrt{2}}+\frac{1}{2 \sqrt{2}}\right)=\left(\frac{\sqrt{3}+1}{2 \sqrt{2}}\right)$