Question

arctanx (tanx)=1?

Answer 1

yup

Answer 2

yes

Answer 3

thanks

Answer 4

(x/y)(y/x)=1, cancellation

Answer 5

lol good job soxhl.... too long username

Answer 6

what???

Answer 7

are you trying to solve
\[\arctan(\tan(x))=1\] for x or are you saying that it is always the case that
\[\arctan(\tan(x))=1\]?

Answer 8

because the second statement is certainly not true

Answer 9

i just want to know if they cancel i am new with the english language

Answer 10

no you cannot "cancel"

Answer 11

if
\[\frac{\pi}{2}\leq x\leq \frac{\pi}{2}\] then
\[\arctan(\tan(x))=x\]

Answer 12

arctangent is the inverse function of tangent. the "identity" function is not 1, that is the identity under multiplication.

Answer 13

the identity function is
\[I(x)=x\]

Answer 14

arctanx(tanx)=arctan(x)tan(x)=xy/yx=1

Answer 15

no sorry.

Answer 16

arctan(x) means the number between -pi/2 and pi/2 whose tangent is x

Answer 17

oh. that's for cot :))))))

Answer 18

no it is not for cotangent either

Answer 19

cot=x/y, tan=y/x

Answer 20

unless you mean to say that
\[\cot(x)\times \tan(x)=1\] which is true. the question was about composition of functions, not multiplication

Answer 21

arctanx (tanx)=1. i'ts what the person typed

Answer 22

what is the derivative of arctan(sec x)

Answer 23

chain rule annoying problem

Answer 24

the derivative of arctan(x) is
\[\frac{1}{x^2+1}\] so the derivative of
\[\arctan(sec(x))=\frac{1}{\sec^2(x)+1}\times \frac{d}{dx}\sec(x)\]

Answer 25

and
\[\frac{d}{dx}\sec(x)=\tan(x)\sec(x)\]

Answer 26

so you get
\[\frac{\tan(x)\sec(x)}{\sec^2(x)+1}\] which can be written is several different ways

Answer 27

thanks a lot