If sin (A – B) = 1/2, cos(A + B) = 1/2; 0^o<A+B<90^o; A > B, find A and B.

Given :

⇒ Sin(A-B) = sin (30 ^o)

On equating both the sides, we get

A - B = 30 ^o …(1)

And

⇒ cos(A + B) = cos (60 ^o)

On equating both the sides, we get

A + B = 60 ^o …(2)

On Adding Eq. (1) and (2), we get

2A = 90 ^o

⇒ A = 45 ^o

Now, Putting the value of A in Eq.(2), we get

45 ^o + B =60 ^o

⇒ B = 15 ^o

Hence, A = 45 ^o and B = 15 ^o