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

(Given 0° < A, B < 90°)

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