If sin (A - B) = $\frac{1}{2}$ and cos (A + B) = $\frac{1}{2}$, $0^\circ$ B then values of A and B are ______.

Question

If sin (A - B) = $\frac{1}{2}$ and cos (A + B) = $\frac{1}{2}$, $0^\circ$ < (A + B) $\leq$ $90^\circ$ and A > B then values of A and B are ______.

KollegeApply · Accepted Answer

If sin (A - B) = $\frac{1}{2}$ and cos (A + B) = $\frac{1}{2}$, $0^\circ$ < (A + B) $\leq$ $90^\circ$ and A > B then values of A and B are ($45^\circ$, $15^\circ$). Explanation: `sin (A - B) = $\frac{1}{2}$ = sin 30^circ, cos (A + B) = $\frac{1}{2}$ = cos 60^circ`. $\therefore$ {A – B = $30^\circ$ and A + B = $60^\circ$} $\Rightarrow$ (A = $45^\circ$, B = $15^\circ$)

AChoose Your Answer