Question

If Sin(A-B) = root 3/2 and Cos (A - B) = root 3/2,where 0°<A+B<90° and A > B, find A and B
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Answer 1

$\sin(a + b) = \frac{ \sqrt{3} }{2} \\ \cos(a - b) = \frac{ \sqrt{3} }{2} \\ \sin(a + b) = \sin(60) \\ \cos(a - b) = \cos(3 0 ) \\ a + b = 60 ......(1)\\ a - b = 30.....(2) \\ adding \: both \: equations \: we \: get \\ 2a = 90 \\ a = 45 \: \\ on \: further \: solving \: we \: get \: b \: = 45$