Derive the relations between these functions by using similar triangles.
By similar triangles, the ratio of BD to BO, sin to 1 is the same as the ratio of CB to OC, tan to sec, and of OB to AO (1 to csc), and of CO to AC (sec to (tan + cot)), and of CD to BC ((sec- cos) to tan), and of OE to BO (sin to 1)
This tells us
so that on taking complements we have as well,
We also get
and the complementary result