If A and B are positive acute angles satisfying 3 ² A+2 ² B=4 and 3 A B = 2 B A Then the value of A +2 ~B is equal to :

Step-by-step solution

Given, 3 ² ~A +2 ² ~B =4 2 ² ~B -1=4-3 ² ~A -1 2 ~B =3 (1- ² ~A )=3 ² ~A (1) and 2 B B =3 A A 2 ~B =3 A A Now, ( A +2 ~B )= A 2 ~B - A 2 ~B = A (3 ² A )- A(3 A A)=0 [using eqs. (1) and (2)] A+2 B= 2