# Differentiating :calculus theory

1. Dec 7, 2011

### chapsticks

1. The problem statement, all variables and given/known data

Verify the identity:

arctanx + arctan(1/x)=∏/2

using calculus theory.
(Hint: Differentiate the left hand side of the identity)

2. Relevant equations

?

3. The attempt at a solution
is this correct?

tan(arctanx + arctan(1/x))
= [tan(arctan(x)) + tan(arctan(1/x))][1 - tan(arctan(x))*tan(arctan(1/x))]

= [x + 1/x]/[1 - x*1/x] = (x + 1/x)/0 = oo

tan pi/2 = oo

2. Dec 7, 2011

### Quinzio

mmm.... they wanted you to do this:
$$\frac{1}{1+x^2}+ etc....$$

3. Dec 7, 2011

### chapsticks

where did that come from I'm confused??

4. Dec 7, 2011

### Staff: Mentor

Start by using the hint, which is to differentiate the left side.

5. Dec 7, 2011

### chapsticks

f'(x)=1/(1+x2) + -1/(x2+1) =0

for all x≠0

function is constant on domain

is this right?

6. Dec 7, 2011

### Dick

Yes, it is. I guessing they meant to specify x>0. Now just pick a nice value of x to put in to figure out what the constant is.