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just olya [345]
3 years ago
6

Sin7x - sin3x cos 7x - cos3x

Mathematics
1 answer:
charle [14.2K]3 years ago
5 0

Answer:

= -cot5x

Step-by-step 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

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