In the given equation, 1 + sin2 A = 3 sin A cosA Dividing both sides by cos2 A We get
1
cos2A
+
sin2A
cos2A
= 3 ,
sinA
cosA
⇒ sec2A+tan2A = 3tanA 1+tan2A+tan2A = 3 tan A ⇒ 2tan A - 3 tan A +1 = 0 ⇒ 2tan2A - 2 tan A - tan A + 1 = 0 ⇒ 2 tan A (tan A - 1) - 1 (tan A - 1) = 0 ⇒ (2tan A - 1) (tan A - 1) = 0 ⇒ tan A =