Calculus/calc

Advertisement

Expert: - 3/30/2009


Question
hi im acctually have trouble with a couple problems and i'm hoping you will be able to run through them step by step so i can understand it: THEIR THE PROVIDE THE IDENTITY:
1. SEC^2X-TAN^2=1
2. SIN^2X/(1-COSX)^2=1+COSX/1-COSX
3. COS^3X/1+SINX=1-SINX/SEC

AND THE FINAL ONE IS  FIND THE EXACT VALUE OF TAN(-PIE/12) IN RADICAL FORM.
THANK YOU!

Answer
1. To make the left side look like 1,
note that sec²x is 1/cos²x and tan²x is sin²x/cos²x.

Combing both of these gives us (1-sin²x)/cos²x.

Note that sin²x + cos²x = 1, so 1 - sin²x = cos²x.

This makes the top cos²x.
What we then have is cos²x/cos²x, which  is 1.

2. To make the right side look like the left, we'll start by
multipling (1+cosx)/(1-cosx) by (1-cosx)/(1-cosx).
The fraction on the right that was (1+cosx)/(1-cosx) is then
(1+cosx)(1-cosx)/(1-cosx)².

Multiplying the top out gives us (1-cos²x)/(1-cosx).
Now note from the identiyt sin²x + cos²x = 1 ,
it can be seen that the top is really sin²x.

What we have then is sin²x/(1-cosx), and that looks like the left.

3. To show that cos^3x/(1+sinx) = (1-sinx)/secx,
multiply the right side by (1+sinx)/(1+sinx) giving us
(1+sinx)(1-sinx)/((1+sinx)secx).

Note that (1+sinx)(1-sinx) = 1 – sin²x = cos²x, so from
(1+sinx)(1-sinx)/((1+sinx)secx), we now have cos²x/((1+sinx)secx).

The last thing to note is that 1/secx = cosx,
so now the equation that was cos²x/((1+sinx)secx) turns into
cos^x(3)/(1+sinx), which is what the left looks like ☺☺☺!

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2012 About.com, a part of The New York Times Company. All rights reserved.