If $\sin ( A - B )=\frac{1}{2}, \cos ( A + B )=\frac{1}{2}, 0^{\circ} < A + B \leq 90^{\circ}, A > B ,$ find $A$ and $B$
If $\sin ( A - B )=\frac{1}{2}, \cos ( A + B )=\frac{1}{2}, 0^{\circ} < A + B \leq 90^{\circ}, A > B ,$ find $A$ and $B$
since, $\sin ( A - B )=\frac{1}{2},$ therefore, $A - B =30^{\circ}$ ......$(1)$
Also, since $\cos ( A + B )=\frac{1}{2},$ therefore, $A + B =60^{\circ}$ ......$(2)$
Solving $(1)$ and $(2),$ we get $: A=45^{\circ}$ and $B=15^{\circ} .$
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