Q. 44.4( 31 Votes )

If 1+sin2θ =3sinθ cos θ, then prove that tanθ =1 or .

Answer :

Given: 1+sin2 θ = 3 sin θ cos θ

Dividing L.H.S and R.H.S equations with sin2 θ,


We get




cot2 θ +1+1 = 3 cot θ [, cosec2 θ – cot2 θ = 1 cosec2 θ = cot2 θ +1]


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



Hence, proved.


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