Question

. If 1 + sin2θ = 3 sinθ cosθ, then find tanθ​

Answer 1

Answer:

Dividing L.H.S and R.H.S equations with sin2 θ, We get, cosec2 θ + 1 = 3 cot θ Since, cosec2 θ – cot2 θ = 1 ⇒ cosec2 θ = cot2 θ +1 ⇒ cot2 θ +1+1 = 3 cot θ ⇒ cot2 θ +2 = 3 cot θ ⇒ cot2 θ –3 cot θ +2 = 0 Splitting the middle term and then solving the equation, ⇒ cot2 θ – cot θ –2 cot θ +2 = 0 ⇒ cot θ(cot θ -1)–2(cot θ +1) = 0 ⇒ (cot θ – 1)(cot θ – 2) = 0 ⇒ cot θ = 1, 2 Since, tan θ = 1/cot θ tan θ = 1, ½ Hence, proved.