Question

If tan (A + B) = √3 and tan (A – B) = 1 √3 ; 0° < + ≤ 90° ; A > , find A and B.​

Answer 1

$\sf \: tan (A + B) = \sqrt{3}⟹ A + B = 60°....(i)$

$\sf \: tan (A - B) = \large \frac{1}{ \sqrt{3} } \small ⟹A - B = 30 \degree...(ii)$

$\sf \: From \: Eqn. (i) + Eqn.(ii),$

$\sf \: We \: have$

$\sf2A = 90 ⟹ \: = \color{red}45°$

$\sf \: From \: eqn. (i),$

$\sf A + B = 60°$

$\sf45° + B = 60°$

$\sf∴ B = \color{red}15$