# Math Help - tan

1. ## tan

Hi all,

I was wondering if i could get this confirmed...

does arctan(x + tan(5*pi)) = arctan(x) + 5*pi?????

ArTiCk

2. Originally Posted by ArTiCK
Hi all,

I was wondering if i could get this confirmed...

does arctan(x + tan(5*pi)) = arctan(x) + 5*pi?????

ArTiCk
Clearly not. Since tan(5 pi) = 0 the left hand side is just arctan x .....

3. Originally Posted by ArTiCK
Hi all,

I was wondering if i could get this confirmed...

does arctan(x + tan(5*pi)) = arctan(x) + 5*pi?????

ArTiCk
Not in general, no. The inverse tangent function is not linear. That is to say defining $f(x) = atn(x)$ then
$f(x + y) = f(x) + f(y)$
is not true for all x and y.

-Dan

4. I don't see why it would, because tan(5pi) is also tan(0), tan(pi), tan(2pi)... etc.

5. Originally Posted by ArTiCK
Hi all,

I was wondering if i could get this confirmed...

does arctan(x + tan(5*pi)) = arctan(x) + 5*pi?????

ArTiCk
IT can be clearly seen that this is untrue by looking at the integral case of each

$\arctan(x+5\pi)=\int\frac{dx}{1+(5\pi+{x})^2}dx$

and the other given by

$\arctan(x)+5\pi=\int\frac{dx}{1+x^2}+5\pi$

From there I think it can become obvious