2arctan(7)+arctan(31/17)

[sintesi]

I need some help to explain a solution to a problem

2arctan(7)+arctan(31/17)

I will skip some steps in the calculation, but so far I've got

tan x = tan(2arctan(7) + arctan(31/17))
...
tan x = (625/408)/(625/408) = 1
x = (pi/4)
...
2arctan(7)+arctan(31/17) = (pi/4)+n*pi

But this is only true for n=1. Why is that? I can't find a good way to explain it.

Thanks in advance

 

[Deleted member 4993]

I need some help to explain a solution to a problem

2arctan(7)+arctan(31/17)

I will skip some steps in the calculation, but so far I've got

tan x = tan(2arctan(7) + arctan(31/17))
...
tan x = (625/408)/(625/408) = 1
x = (pi/4)
...
2arctan(7)+arctan(31/17) = (pi/4)+n*pi

But this is only true for n=1. <-- what makes you say that (even though it is correct)?

What is the range of arctan(x) function?

 

[sintesi]

What is the range of arctan(x) function?

[-pi/2, pi/2] ?

This is where it doesn't add up for me because 5pi/4 is greater than pi/2. Maybe I'm just confused

 

[Deleted member 4993]

In this case, the answer is sum of two angles - one in second quadrant (after being multiplied by 2) and the other in first quadrant.

You still did not tell me - why did you think only n=1 is valid answer.

 

[sintesi]

In this case, the answer is sum of two angles - one in second quadrant (after being multiplied by 2) and the other in first quadrant.

You still did not tell me - why did you think only n=1 is valid answer.

Oh sorry. I just had the answer from the beginning. Just didn't understand it.Thanks!