201k views
7 votes
Sin7x - sin3x
cos 7x - cos3x

Sin7x - sin3x cos 7x - cos3x-example-1
User Pw
by
8.5k points

1 Answer

3 votes

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

User Takeshin
by
8.5k points

Related questions

asked Oct 24, 2024 210k views
Sajas asked Oct 24, 2024
by Sajas
8.2k points
1 answer
1 vote
210k views
asked Apr 25, 2024 56.9k views
David DV asked Apr 25, 2024
by David DV
8.8k points
1 answer
0 votes
56.9k views
asked Sep 15, 2015 84.9k views
SlothOverlord asked Sep 15, 2015
by SlothOverlord
7.7k points
1 answer
2 votes
84.9k views