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

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

Answer»

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

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