Hey,(adsbygoogle = window.adsbygoogle || []).push({});

I came across this 'identity' today and was wondering if there was any algebraical explanation to this...

Basically I had to show:

[tex]\arctan( \frac{a}{b}) + \arctan( \frac{b}{a}) = \frac{\pi}{2}[/tex]

(And if necessary, (a,b) > 0 )

It is pretty easy to show when you draw a right triangle:

(a and b are the sides while c and d are the angles)Code (Text):/|

/c|

/ |

/ |a

/d |

/_____|

b

Now, [tex]\tan d = \frac{a}{b}[/tex] and [tex]\tan c = \frac{b}{a}[/tex] and because it is a right triangle, [tex]c + d = \frac{\pi}{2} = \arctan( \frac{a}{b}) + \arctan( \frac{b}{a})[/tex].

But I was wondering if you can also proof this algebraically?

I typed it into Maple and got [tex]\frac{1}{2} \text{signum}(\frac{a}{b}) \pi[/tex]. If my memory serves me well, signum is always 1 if a/b > 0 and -1 if a/b < 0, so if a/b > 0 this holds...

So yeah, just wondering... I can't see any way to do it algebraically...

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Atan(a/b) + atan(b/a) = pi/2

Loading...

Similar Threads - Atan atan | Date |
---|---|

Identities for atan(a+b) or atan(a*b) | Aug 12, 2011 |

**Physics Forums - The Fusion of Science and Community**