AllExperts > Experts 
Search      

Advanced Math

Volunteer
Answers to thousands of questions
 Home · More Questions · Answer Library  · Encyclopedia ·
More Advanced Math Answers
Question Library

Ask a question about Advanced Math
Volunteer
Experts of the Month
Expert Login

Awards

About Us
Tell friends
Link to Us
Disclaimer

 
 
 
 
About Sherman D.
Expertise
I can answer questions dealing in mathematics of all kinds except for Physics and Calculus, but i can answer questions in Pre-Calculus and Chemistry. I can also answer questions in Recipes of all kinds. I can find games cheats/walkthroughs, but i can`t find a specific game online or offline. I can also do history and recipes for alcoholic beverages.

Experience
Mathematics, Recipes, History, and Games.

Education/Credentials
High School graduated. I graduated with honors, and i was in Beta Club for a year and a half.

Awards and Honors
Principle's list and A and B honor roll in high school only.

 
   

You are here:  Experts > Science > Mathematics > Advanced Math > Trig Identity (Prove Equal to one side)

Topic: Advanced Math



Expert: Sherman D.
Date: 5/10/2008
Subject: Trig Identity (Prove Equal to one side)

Question
I've spent a lot of time working on this problem and i've gotten close but it never comes out right. Here's the question: 3cosX-cotX = (3-cscX)/secX  

Answer
3cos(x) - cot(x) = (3 - csc(x))/(sec(x))

(3 - csc(x))/(sec(x)) =
(3 - csc(x))/(1/cos(x)) =
(3 - csc(x))cos(x) =

Just so there is no confusion, (a / b/c) is the same as saying (a/1)/(b/c) so you just do this (a/1)(b/c)

3cos(x) - (csc(x)cos(x))

3cos(x) - ((1/sin(x))cos(x))

3cos(x) - (cos(x)/sin(x))

3cos(x) - cot(x)

if you do this the long way for ex:

(3 - (1/sin(x)))/(1/cos(x)) =
((3sin(x) - 1)/sin(x))/(1/cos(x)) =
((3sin(x) - 1)/sin(x))cos(x) =
(3sin(x)cos(x) - cos(x))/sin(x)
3cos(x) - (cos(x)/sin(x))
3cos(x) - cot(x)

--------------------------------------

and if you solved the left side first and not the right side first.

3cos(x) - cot(x)
3cos(x) - (cos(x)/sin(x))
(3sin(x)cos(x) - cos(x))/sin(x)

this is probably where you had the trouble. If so, here is a tip.

Sometimes you have to solve the left, right, or both sides. If one doesn't work, try the other, if the other doesn't work after you have tried that side, then try both, and if that doesn't work, either you did something wrong, need to change something, like cos(2x) can equal 3 different things and still mean the same, or you can only solve for x.

For a graph to see if one side does in fact match the other side, go to http://www.calculator.com/calcs/GCalc.html

you would have to type in your problem like this 3cos(x) - cot(x), click enter on the keyboard, then try the other side like this (3 - csc(x))/sec(x)

and don't worry, it will understand cot(x), sec(x), and csc(x). also if you have square roots, you can right them like x^(1/2) or sqrt(x), but when graphing, don't forget you have a +sqrt(x) and a -sqrt(x), also with the +sqrt(x) you don't need the +, but with -sqrt(x) you do need the -, the graph won't do both sides, it only understands sqrt(x) as being positive.

more info on what trigs equal, go to http://math2.org/math/trig/identities.htm


Add to this Answer    Ask a Question



  Rate this Answer
   Was this answer helpful?
Not at allDefinitely              
   12345  

     
About Us | Advertise on This Site | User Agreement | Privacy Policy | Help
Copyright  © 2008 About, Inc. About and About.com are registered trademarks of About, Inc. The About logo is a trademark of About, Inc. All rights reserved.