Question

If sin(A +B) = 1(A -B) = 1, find A and B.

Answer 1

sin(A +B) = 1
⇒ sin(A + B) = sin90°
⇒ A + B = 90° .....(i)
cos(A - B) = 1
⇒ cos(A - B) = cos0°
⇒ A - B = 0° ........(ii)
Adding (i) and (ii)
A + B +A - B= 90° + 0
2A = 90°
A = 45°
Substituitng value of A in (i)
A + B = 90°
45° + B = 90°°
B = 45°
Therefore,
A = B = 45°.