Q. 105.0( 2 Votes )

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


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