Solution :
The formula of sin C – sin D is 2 sin(\(C – D\over 2\)) cos(\(C + D\over 2\)).
Example : Express sin \(6\theta\) – sin \(2\theta\) as a product.
Solution : We have,
sin \(6\theta\) – sin \(2\theta\) = 2 sin(\(6\theta – 2\theta\over 2\)) cos(\(6\theta + 2\theta\over 2\))
= 2 sin \(2\theta\) cos \(4\theta\)