Question

Find the measure of angles A and B in the following, where A and B are acute.

cos `((A + B)/2) = 1/ sqrt2 and 2 sin (A − B) = 1`

Answer 1

Given:

cos `((A + B)/2) = 1/ sqrt2 and 2 sin (A − B) = 1`

Since 0° < `(A + B)/2 <  90°`, We must have `(A + B)/2 = 45°`

= A + B = 90°

`2 sin (A − B) = 1 = sin (A − B) = 1/2`

with A, B acute, − 90° < (A − B) <  90°, A − B = ± 30°

If A − B = 30° : A = 60°, B = 30°

If A − B = − 30 : A = 30°, B = 60°   ...[both angles are acute]