Question

Tan(A+B) =√3 and Tan(A-B) =1/√3,0<A+B<90°, A>B then find the value of Aand B

Answer 1

tan(A+B)=√3
A+B=60°      (tan 60°=√3)......(1)
tan(A-B)=1/√3
A-B=30°       (tan 30°=√3).......(2)
On solving(1) and (2) equations:-
A+B=60°
+A-B=30°/ 2A=90°
A= 45°
45°+B=60°
B=60°-45°= 15°
Thus,
A=45°
B=15°

Hope this helps you!!

Answer 2

Hey there!
_______________________________________________________________

tan(A+B) = √3                                           tan(A-B) = 1/√3

tan(A-B) = tan 60°--- 1)                             tan(A-B) = tan 30°
     
                                     solving 1 and 2       
 
A + B = 60
A - B   = 30
___________
 2A = 90
 A = 45°

Put eq. 1) in eq. 2)

=) A+ B = 60
=) 45 + B = 60
=) B = 60 - 45
=) B = 15

so, A = 45 and B = 15

Hope this helps u ^_^