Q. 50

If 1+sin2θ = 3 sinθ . cosθ, then prove that tan θ = 1 or 1/2.

Answer :

Given: 1+sin2θ =3 sin θ cos θ

Divide by cos2 θ to both the sides, we get



sec2 θ + tan2 θ = 3 tan θ


1+ tan2 θ+ tan2 θ = 3tan θ


2 tan2 θ –3tan θ +1 = 0


Let tanθ = x


2x2 – 3x +1 = 0


2x2 – 2x – x +1 = 0


2x ( x 1) 1(x 1) = 0


(2x 1)(x 1) = 0


Putting each of the factor = 0, we get


x = 1 or


And above, we let tan θ = x



Hence Proved


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