## mathslover 4 years ago tan A = -1/2 , tan B = -1/3 , then A+B = ?

1. mathslover

@calculusfunctions sir.

2. mathslover

I had come up with : tan (A+B) = -1

3. mathslover

so (A+B) = ?

4. anonymous

A+B = -45 + 180 * k

5. mathslover

is it, 7pi /4

6. anonymous

$\tan(A+B) = \frac{\tan(A) + \tan(B)}{1 - \tan(A) \cdot \tan(B)}$

7. anonymous

-45 = pi/4 180 = pi so -pi/4 + pi = 3pi/4 -pi/4 + 2pi = 7pi/4 and so on..

8. anonymous

If you calculated it right then: $A+B= \tan^{-1}(-1)$

9. anonymous

so 7pi/4 is one possibility

10. anonymous

$A+B = \tan^{-1}\frac{ -1 }{ 2 }+\tan^{-1} \frac{ -1 }{ 3 }$

11. mathslover

so it can be : 3 pi / 4, 7pi/4 , . ... It can not be 5 pi / 4 because it will be positive for tan.

12. mathslover

But the book says that the answer is : d) none Options were : i) pi/4 ii) 3 pi/4 iii) 5 pi/4 iv) none.

13. mathslover

So it will be 3 pi/4 ? or none?

14. hartnn

it will be 3pi/4 are any constraints given?

15. mathslover

constraints?

16. hartnn

like A+B should be between 0 to 90 or something like this ?

17. hartnn

else 3pi/4 is correct

18. mathslover

ok thanks a lot @hartnn :)

19. anonymous

wud tan(A+B) formula work for all angles

20. hartnn

yes.

21. anonymous

ok thank you :D

22. anonymous

$\pi - \frac{\pi}{4} = \frac{3 \pi}{4}$

23. anonymous

There was some mistake in the formula that I had written above.. That day I was looking for the same and now I have found it : $\tan^{-1}(-x) = \pi - \tan^{-1}(x)$