If sin (A + B) = 1 and cos (A – B) = , then find A and B.

Given : sin (A+B) =1

⇒ Sin(A+B) = sin (90 ^o) [∵ sin (90 ^o)=1]

On equating both the sides, we get

A + B = 90 ^o …(1)

And

⇒ cos(A – B) = cos (30 ^o)

On equating both the sides, we get

A – B = 30 ^o …(2)

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

2A = 120 ^o

⇒ A = 60 ^o

Now, Putting the value of A in Eq.(1), we get

60 ^o + B =90 ^o

⇒ B = 30 ^o

Hence, A = 60 ^o and B = 30 ^o