Scale at Latitude = Scale at Equator x 1 / Cosine of Latitude
Scale at 60°S = 1 / 3,704,000 x 1 / Cosine 60°
1 / x = 1 / 3,704,000 x 1 / 0.5
Now if you wish, you can divide 1 by 3,704,000 and 1 by 0.5, then multiply those numbers together to produce x which when divided into 1 will give you an answer of 1,852,000.
1 / x = (2.699 x 10(-7)) x 2
1 /x = (5.399 x 10(-7))
x = 1 / (5.399 x 10(-7))
x = 1,852,000
However, it is far simpler to use only the denominators. which will give you exactly the same answer.
Therefore:
Scale at Latitude = Scale at Equator x 1 / Cosine of Latitude
Scale at 60°S = 1 / 3,704,000 x 1 / Cosine 60°
1 / x = 1 / 3,704,000 x 1 / 0.5
x = 3,704,000 x 0.5 (Use denominators ONLY)
x = 1,852,000