If sin (A - B) = 1/2 and cos (A +B) = 1/2 ,0° < (A + B) < 90° and A > B then find A and B.

Given: (i) sin (A - B) = 1/2


(ii) cos (A + B) = 1/2


Since, sin (A - B) = 1


sin (A - B) = sin 30° ( 0° < (A + B) < 90°, sin 30° = 1/2)


A - B = 30° .......................................... (1)


Also, cos (A + B) = 1/2


cos (A + B) = cos 60° ( 0° < (A + B) < 90°, cos 60° = 1/2)


A + B = 60° .......................................... (2)


On adding equation (1) and (2), we get,


2A = 90° A = 45°


Putting this value in equation (2), we get,


B = 60° - A = 60° - 45° B = 15°


A = 45°, B = 15°


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