Question

If $sin(A+B)=1$ and $sin(A-B)=\frac{1}{2}$, $0\le A+B\le {90}^o$ and $A>B,A>B$, then find A and B.

Answer 1

We have,
$sin(A+B)=1=sin90º$
A + B = 90º -- (i)
(1 Mark)
And
$sin(A-B)=\frac{1}{2}=sin30º$
A - B = 30º -- (ii)
(1 Mark)
Adding (i) + (ii),

We get,
$\Rightarrow 2A=120º\Rightarrow A=60º$
(0.5 Marks)
Substituting value of A in either (i) or (ii), we get $B=30º$. (0.5 Marks)