Trigonometric Functions

Prove that:
4. (cos x – cos y)
2
+ (sin x – sin y)
2
= 4 sin2
2
x y −
5. sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x
6 . (sin7 sin5 ) (sin 9 sin3 ) tan 6
(cos7 cos5 ) (cos9 cos3 )
x x x x
x