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

⇒ cos(A – B) = cos (0 ^o) [∵ cos(0 ^o) = 1]

On equating both the sides, we get

A – B = 0 ^o …(2)

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

2A = 90 ^o

⇒ A = 45 ^o

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

45 ^o + B =90 ^o

⇒ B = 45 ^o

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