# Simple question of calculus

nil1996

## Homework Statement

$\sqrt{\frac{1-cos2x}{1+cos2x}}$
differentiate with respect to x

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 $\frac{tanx}{|tanx|}$sec2x
why??

Homework Helper
Your answer is correct. I don't see the need for your book to specify tanx/tanx in it.

nil1996
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

Homework Helper
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

1 person
nil1996
thanks got it