By: Tao Steven Zheng (鄭濤)

【Problem】

?Indian astronomers used three major trigonometric ratios: “jya” (sine), “koti-jya” (cosine), and “utkrama-jya” (versine). The versine is defined as?

Determine the equivalent expression of the versine in terms of sine.

?

【Solution】

It is known that

Since

it follows that

Therefore,