Given,
sin(A+B)=√32
And,
sin(A−B)=12
We know that,
sin60∘=√32
So, sin60∘=sin(A+B)
On comparing, A + B = 60∘ (i)
We also know that,
sin30∘=12
So, sin30∘=sin(A−B)
On comparing, A - B = 30∘ (ii)
Add equation (i) and equation (ii),
(A + B) + (A - B) = 60 + 30
A + B + A - B = 90
2A = 90
A = 90∘2
A = 45∘
Thus, A = 45∘