Question

HELP!
please prove that
Arctan(-x)= - Arctanx

Answer 1

I'd prolly just do the same thing as the last one :o\[\large\rm y=-\arctan(x)\]\[\large\rm -y=\arctan(x)\]\[\large\rm \tan(-y)=x\]Since tangent is an odd function,\[\large\rm \tan(-y)=-\tan(y)=x\]\[\large\rm \tan(y)=-x\]\[\large\rm y=\arctan(-x)\]

Answer 2

Lot of weird little steps in that though :D

Answer 3

thanks :)))

Answer 4

@zepdrix what do you mean to that the tangent is an odd function?

Answer 5

An odd function satisfies this property:\[\large\rm f(-x)=-f(x)\]Examples:\[\large\rm f(x)=x^3\]\[\large\rm f(-x)=(-x)^3=-(x)^3=-f(x)\]
\[\large\rm g(x)=\sin(x)\]\[\large\rm g(-x)=\sin(-x)=-\sin(x)=-g(x)\]

An even function satisfies this property:\[\large\rm f(-x)=f(x)\]Examples:\[\large\rm f(x)=x^2\]\[\large\rm f(-x)=(-x)^2=(x)^2=f(x)\]
\[\large\rm g(x)=\cos (x)\]\[\large\rm g(-x)=\cos(-x)=\cos(x)=g(x)\]

Answer 6

Tangent is like sine in this respect.

Answer 7

It's good to have an understanding of even and odd functions,
but at the very least make sure you understand the basics that it allows us with trig functions:
`if you have a negative in your cosine, it can disappear`
`if you have a negative in your sine or tangent, it can come outside`

Answer 8

oh my goodness.. thank you so much