# Hello please help me to solve this sum If tanA=2 ,tanB = 3 then find the value of (A+B)

CHAKRAVARTHI
52 Points
6 years ago
GIVEN,
tan A=2
A=tan-1(2)..............(1)  [take it as equation no.1]
AND,
2tan B=3,
B=tan-1(3).............(2)  [take it as equation no.2]

hence ,(1)+(2)= A+B=tan-1(2)+tan-1(3)
pavithra Ayyanar
21 Points
6 years ago
If tanA = 2 and tanB = 3 then
tan(A+B) = tanA+tanB/1-tanAtanB
= 2+3/1-2(3)
= 5/1-6
= 5/-5
= $-1$
A+B= tan-1(-1)
A+B = $-\pi /4$
$The principal value =- \pi /4$
General sol $\theta =n\pi -\pi /4$$n\in Z$
Puneet trivedi
39 Points
5 years ago
TanA=2TanB=3Then,by formulaTan(A+B)=TanA+TanB/1-TanA TanBTan(A+B)=2+3/1-2*3Tan(A+B)=5/-(5)Tan(A+B)=-1Tan(A+B)=Tan(-45)(A+B)=Tan^-1(-45) ans...
Soumendu Majumdar
159 Points
5 years ago
Dear Student,
tan(A + B) = { tan A + tan B }/{ 1 – tan A . tan B }
= ( 2 + 3 )/( 1 – 2 x 3)
= – 1 (Ans)
So (A + B) = $n\Pi + 135^{\circ}$ or  $n\Pi -45^{\circ}$

Hope it helps!
Soumendu Majumdar
159 Points
5 years ago
If you have any more doubts, don’t hesitate, feel free to ask