If $sin (A - B) =\frac{1}{2}$ and $cos(A +B)=\frac{1}{2}$, where A > B > 0° and A + B is an acute angle, then the value of A is:
Answer & explanation
Correct answer: option 1
$sin (A - B) =\frac{1}{2}$
We know, sin30º = \(\frac{1 }{2}\)
So , ( A - B ) = 30º ------(1)
And, cos ( A + B ) = \(\frac{1 }{2}\)
cos 60º = \(\frac{1 }{2}\)
( A + B ) = 60º ------(2)
On Adding 1 and 2
2A = 90º
A = 45º