Question

tan A = -1/2 , tan B = -1/3 , then A+B = ?

Answer 1

@calculusfunctions sir.

Answer 2

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

Answer 3

so (A+B) = ?

Answer 4

A+B = -45 + 180 * k

Answer 5

is it, 7pi /4

Answer 6

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

Answer 7

-45 = pi/4
180 = pi

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

Answer 8

If you calculated it right then:

\[A+B= \tan^{-1}(-1)\]

Answer 9

so 7pi/4 is one possibility

Answer 10

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

Answer 11

so it can be : 3 pi / 4, 7pi/4 , . ...

It can not be 5 pi / 4 because it will be positive for tan.

Answer 12

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.

Answer 13

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

Answer 14

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

Answer 15

constraints?

Answer 16

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

Answer 17

else 3pi/4 is correct

Answer 18

ok thanks a lot @hartnn :)

Answer 19

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

Answer 20

yes.

Answer 21

ok thank you :D

Answer 22

\[\pi - \frac{\pi}{4} = \frac{3 \pi}{4}\]

Answer 23

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 :

\[\tan^{-1}(-x) = \pi - \tan^{-1}(x)\]