If tan (A + B) = $\sqrt{3}$, tan (A - B) = 1 and A, B (B < A) are acute angles, find the values of A and B.

Given,

⇒ tan (A + B) = $\sqrt{3}$

⇒ tan (A + B) = tan 60°

⇒ A + B = 60° ……….(1)

⇒ tan (A - B) = 1

⇒ tan (A - B) = tan 45°

⇒ A - B = 45° ……….(2)

Adding (1) and (2) we get :

⇒ A + B + A - B = 60° + 45°

⇒ 2A = 105°

⇒ A = $\dfrac{105}{2}$

⇒ A = $52\dfrac{1}{2}\degree$

Substituting value of A in (2) we get :

⇒ $\dfrac{105}{2}$ - B = 45°

⇒ B = $\dfrac{105}{2}$ - 45°

⇒ B = $\dfrac{105 - 90}{2}$

⇒ B = $\dfrac{15}{2}$

⇒ B = $7\dfrac{1}{2}\degree$

Hence, A = $52\dfrac{1}{2}\degree$ and B = $7\dfrac{1}{2}\degree$