Question

2 cos 37° 30× cos 7° 30​

Answer 1

$2\cos37^\circ30'\cdot\cos7^\circ30'=2\cdot\dfrac{1}{2}\left(\cos(37^\circ30'-7^\circ30')+\cos(37^\circ30'+7^\circ30')\right)=\\=\cos30^\circ+\cos45^\circ=\dfrac{\sqrt{3}}{2}+\dfrac{\sqrt{2}}{2}=\dfrac{\sqrt{3}+\sqrt{2}}{2}$