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Derive the relations between these functions by using similar triangles.

Solution:

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: