Verified answer

there is a formula:

sinAsinB = ½(cos(A-B) - cos(A+B))

Which means 2sinAsinB = cos(A-B) - cos(A+B)

So we can use the formula with A = 82.5° and B = 37.5° as follows:

2 sin 82.5° sin 37.5° = cos(82.5°-37.5°) - cos(82.5°+37.5°)

= cos 45° - cos 120°

= √2/2 - -½

= √2/2 + ½