Question

If tan (A + B) = $\sqrt3$ and tan (A - B) = $\frac{1}{\sqrt3}$; 0°$<$ (A + B) $≤$ 90° ; A > B, find A and B

Answer 1

tan (A + B) = $\sqrt3$
$⇒$ tan (A + B) = 60°
$⇒$ A + B = 60 … (1)

tan (A - B) = $\frac{1}{\sqrt3}$
$⇒$ tan (A - B) = tan 30
$⇒$ A - B = 30 … (2)
On adding both equations, we obtain
2A = 90
$⇒$ A = 45 From equation (1), we obtain
45 + B = 60
B = 15
Therefore, $∠$ A = 45° and $∠$ B = 15°