Question

If `tan(A - B) = (1)/sqrt(3)` and `tan(A + B) = sqrt(3)`, find A and B.

Answer 1

`tan (A - B) = (1)/sqrt(3)`

⇒ tan (A – B) = tan 30°

⇒ A – B = 30°   ...(i)

`tan (A + B) = sqrt(3)`

⇒ tan (A + B) = tan 60°

⇒ A + B = 60°   ...(ii)

Adding (i) and (ii)

A – B + A + B = 30° + 60°

⇒ 2A = 90°

⇒ A = 45°

Substituting the value of A in (i)

A – B = 30°

45° – B = 30°

B = 15°

Therefore, A = 45° and B = 15°.