An equilateral triangle T with vertices ABC is drawn inside a rectangle APQR so that B lies on the line PQ and C lies on the line QR. The angle PAB is 10^o.

How can you use this diagram to prove that cos 20^o = cos 40^o + cos 80^o?

Find and prove a similar relationship between sin 20^o, sin 40^o and sin 80^o.

Can you find general versions of these results, both for sines and for cosines? What are they?