Simple Calculus Question: Differentiating Square Root Fraction

  • Thread starter Thread starter nil1996
  • Start date Start date
  • Tags Tags
    Calculus
Click For Summary

Homework Help Overview

The problem involves differentiating the expression \(\sqrt{\frac{1-\cos 2x}{1+\cos 2x}}\) with respect to \(x\). The subject area is calculus, specifically focusing on differentiation techniques and trigonometric identities.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to simplify the expression using substitutions related to trigonometric identities. They express confusion regarding the difference between their result and the textbook's answer, which includes a modulus function.

Discussion Status

Some participants affirm the original poster's result, questioning the necessity of the modulus in the textbook's answer. Others suggest that the inclusion of the modulus may relate to considerations of the square root and its implications for differentiating the expression.

Contextual Notes

There is a discussion about the implications of the modulus of \(\tan x\) in the context of the square root, as well as the conditions under which \(|\tan x|\) simplifies to \(\tan x\).

nil1996
Messages
301
Reaction score
7

Homework Statement



[itex]\sqrt{\frac{1-cos2x}{1+cos2x}}[/itex]
differentiate with respect to x

Homework Equations



none

The Attempt at a Solution



i have simplified it by substituting cos2x as 1-2sin2x and 2cos2x-1

I have got the answer as sec2x but my textbook says the ans is [itex]\frac{tanx}{|tanx|}[/itex]sec2x
why??

please help
 
Physics news on Phys.org
Your answer is correct. I don't see the need for your book to specify tanx/tanx in it.
 
rock.freak667 said:
I don't see the need for your book to specify tanx/tanx in it.

it is tanx/|tanx|
the denominator is mod of tanx
 
nil1996 said:
it is tanx/|tanx|
the denominator is mod of tanx

Yes well the main point was that for x>0, |tanx| = tanx so it would cancel out to give you sec2x.

The only reason I can think of to specify something like that is if you accounted for taking the square root of the radical.

Meaning that your expression would simplify to √(tan2x) = ± tanx

and d/dx(± tanx) = ± sec2x
 
  • Like
Likes   Reactions: 1 person
thanks got it
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
Replies
4
Views
2K
Replies
28
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
6
Views
2K