# 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

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