Answer:
= -cot5x
Explanation:
sin7x - sin3x = sin(5x + 2x) - sin(5x - 2x)
= [sin5x cos2x + cos5x sin2x] - [sin5x cos2x - cos5x sin2x]
= 2 cos5x sin2x
cos7x - cos3x = cos(5x + 2x) - cos(5x - 2x)
= [cos5x cos2x - sin5x sin2x ] - [cos5x cos2x + sin5x sin2x]
= -2 sin5x sin2x
so
(sin7x - sin3x)/(cos7x - cos3x)
= -cos5x/sin5x = -cot5x