It's a little easier to prove 'Sin(a-b)=sinacosb - cosasinb'
(and then change the sign on b).
The basic idea is to set up the points whose coordinates are
(cos(a),sin(a)) (i.e. the point a distance a from (0,0) measured along the circle) and (cos(b),sin(b)) and calculate the straight line distance between them (the arc distance, along the circle, is a-b, of course.) Now mark the point whose arc length from (1,0) is also a-b: it's coordinates are (cos(a-b), sin(a-b)) and calculate the straight line distance beween it and (1,0). Since the arclengths are the same, the lengths of these chords are the same. Set the two calculations equal and "grind".
We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling We Value Civility
• Positive and compassionate attitudes
• Patience while debating We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving