By: Tao Steven Zheng (郑涛)

【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,