If tan A = 1 x x 2 + x + 1 , tan B = x x 2 + x + 1 and tan C = x − 3 + x − 2 + x − 1 1 2 , 0 A , B , C π 2 , then A + B is equal to:

Question

If tan A = 1 x x 2 + x + 1 , tan B = x x 2 + x + 1 and tan C = x − 3 + x − 2 + x − 1 1 2 , 0 A , B , C π 2 , then A + B is equal to:, C, π − C, 2 π − C, π 2 − C

MARKS App · Accepted Answer

Given, tan A = 1 x x 2 + x + 1 , tan B = x x 2 + x + 1 and tan C = x − 3 + x − 2 + x − 1 1 2 = 1 + x + x 2 x x We know that, tan A + B = tan A + tan B 1 − tan A tan B ⇒ tan A + B = 1 x x 2 + x + 1 + x x 2 + x + 1 1 − 1 x 2 + x + 1 ⇒ tan A + B = 1 + x x 2 + x + 1 x 2 + x x ⇒ tan A + B = 1 + x x 2 + x + 1 x 2 + x x ⇒ tan A + B = x 2 + x + 1 x x ⇒ tan A + B = tan C ⇒ A + B = C

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