Top Posters
Since Sunday
s
5
g
5
K
5
o
5
g
5
o
4
k
4
s
4
I
4
k
4
j
4
o
4
Home Q & A Board Science-Related Homework Help Mathematics
New Topic  
tonichilds83 tonichilds83
wrote...
Go to Answer
Posts: 64
Rep: 1 0
11 years ago
"use properties of the trigonometric functions to find the exact value of each expression. Do not use a Calculator"

sec^2(18) - tan^2(18)
Read 419 times
6 Replies
Replies
Answer accepted by topic starter
iloveanatomyiloveanatomy
wrote...
#1
Posts: 46
Rep: 1 0
11 years ago
Sign in or Sign up in seconds to unlock everything for free
1

Related Topics

wrote...
#2
11 years ago
Remember that sec^2(x) - tan^2(x) = 1 for any x. So, sec^2(18) - tan^2(18) = 1.

Hope this helps.
wrote...
#3
11 years ago
Recall that sec = 1/cos, tan = sin/cos. So we can rewrite the problem as:

1 / cos^2(18)     -     sin^2(18) / cos^2(18)

Pulling the 1/cos^2 out, we get:

(1 - sin^2(18) ) / cos^2(18)

It is a known trig property that:
cos^2(x) + sin^2(x) = 1. This implies cos^2(x) = 1 - sin^2(x)

So this simplifies to cos^2(18) / cos^2(18) = 1.
wrote...
#4
11 years ago
Use identity 1+tan^2(x) = sec^2(x)

sec^2(18) - tan^2(18)
=1+tan^2(18) - tan^2(18)
=1
wrote...
#5
11 years ago
since sec=1/cos and tan=sin/cos
sec^(18)-tan^2(18)=1/cos^2 18 -sin^2 18/cos^2 18
=1-sin^2 18/cos^2 18    ...... 1-sin^2=cos^2
=cos^2 18/cos^2 18 = 1
wrote...
#6
11 years ago
Remember that! sec^2 x = tan^2 x + 1 so

sec^2 (18) - tan^2 (18) =
tan^2 (18) + 1 - tan^2 (18) = 1
New Topic      
Quick Reply
Explore
Post your homework questions and get free online help from our incredible volunteers
  910 People Browsing
Start New Topic Take the Tour CoursesNew Study Tools Topics Trending Browse by Textbook
Live Chat
Related Images
  
 355
  
 358
  
 296