Math Help - Integration problem calculus

1. Integration problem calculus

Hi, I needed some help with this math problem. A solution would be really appreciated.

If , then there is a unique real number such that

Express as a rational function of and .

2. Re: Integration problem calculus

Originally Posted by danny88
, then there is a unique real number such that

Express as a rational function of and .

Hints: you have $\arctan(x)+\arctan(y)=\arctan(z)$

So $\tan(a+b)=z$

3. Re: Integration problem calculus

I really don't get the next step

4. Re: Integration problem calculus

Originally Posted by danny88
I really don't get the next step

What is $\tan(a+b)=$

5. Re: Integration problem calculus

sin(A+B)/cos(A+B)

6. Re: Integration problem calculus

Originally Posted by danny88
sin(A+B)/cos(A+B)

That does you no good!

$\tan(a+b)=\frac{\tan(a)+\tan(b)}{1-\tan(a)\tan(b)}$.

Clearly $a=\arctan(x)$.

If you are still confused, then it is time to leave this site and seek live instruction from your instructor.

Thank you