Top Posters
Since Sunday
g
3
3
2
J
2
p
2
m
2
h
2
s
2
r
2
d
2
l
2
a
2
Home Q & A Board Science-Related Homework Help Mathematics
New Topic  
riverviewguit riverviewguit
wrote...
Go to Answer
Posts: 59
Rep: 0 0
11 years ago
The equation is y = (1 + cos^2x) / (1 - cos^2x)

The answer is supposed to be (4cosx) / (sin^3x)

Can somebody SHOW me how it is done, step by step? I know this involves the quotient rule, but I just can't figure it out. Any help is much appreciated.
Thanks for the help, I didn't properly recognize the part where 1 = sin^2 + cos^2.

And yes you guys are right, I forgot to add a - in front of the answer
Read 438 times
2 Replies
Replies
wrote...
#1
11 years ago
y = (1 + cos^2(x)) / (1 - cos^2(x)

recall that 1 - cos^2(x) = sin^2(x)

Thus y = (1 + cos^2(x)) / sin^2(x)

split the fraction

y = ( 1 / sin^2(x))  + ( cos^2(x) / sin^2(x))

y = csc^2(x) + cot^2(x)

now differtentiate

y '  = 2 csc x ( - csc x cot x ) + 2cot x (- csc^2(x)

= -4 cot x  csc^2(x)

= - 4 (cos x / sin x)(1 / sin^2(x)

= - 4cos x / sin^3(x)
Answer accepted by topic starter
RiyanRiyan
wrote...
#2
Posts: 47
Rep: 0 0
11 years ago
Sign in or Sign up in seconds to unlock everything for free
This verified answer contains over 130 words.
1

Related Topics
New Topic      
Quick Reply
Explore
Post your homework questions and get free online help from our incredible volunteers
  1140 People Browsing
 114 Signed Up Today
Start New Topic Take the Tour CoursesNew Study Tools Topics Trending Browse by Textbook
Live Chat
Related Images
  
 181
  
 1030
  
 1607
Your Opinion
Who's your favorite biologist?
Votes: 586
Previous poll results: Which 'study break' activity do you find most distracting?