If cos (A + B) = 0 and sin (A - B) = $\frac{1}{2}$, then the value of B is : (Given 0° < A, B < 90°)

45° 90° 60° 30°

30°

Given :- cos (A + B) = 0 and sin (A - B) = \(\frac{1 }{2}\) { we know,  cos 90º = 0   & sin 30º = \(\frac{1 }{2}\) } So, A + B = 90º    -----(1) A - B = 30º     -----(2) On adding 1 and 2. 2A = 120º  A = 60º  Putting value of A into equation1. 60º  + B = 90º  B = 30º