An acute angled triangle ABC, If sin2(A + B - C) = 1 and tan (B + C - A) = √3, then the value of angle ∠B is -

দেওয়া আছে,
sin2(A + B + C) = 1
⇒ sin 2(A + B + C) = sin 90°
⇒ 2(A + B + C) = 90°
∴ (A + B + C) = 45°............(i)
আবার, tan (B + C - A) = √3
⇒ tan (B + C - A) = tan60°(tan 60° = √3)
B + C - A = 60°............(ii)
এখন, (i) ও (ii) নং সমীকরণ যোগ করে পাই,
(A + B - C) + (B + C - A) = 45° + 60°
⇒2B = 105°
⇒ B = 52(1/2)°