Find the general solution for 3tan^2θ-2sinθ=0

Steps to solve Find the general solution for 3tan^2θ-2sinθ=0

⇒3tan^2θ-2sinθ=0

⇒3(sin^2θ/cos^2θ)-2sinθ=0

⇒3sin^2θ-cos^2θ.2sinθ/cos^2θ=0

⇒3sin^2θ-cos^2θ.2sinθ=0

⇒3sin^2θ-(1-sin^2θ).2sinθ=0

⇒3sin^2θ+2sin^3θ-2sinθ=0

⇒sinθ(3sinθ+2sin^2θ-2)=0

⇒sinθ=0 OR 3sinθ+2sin^2θ-2=0[Impossible]

⇒θ=nπ

Hence the general solution for 3tan^2θ-2sinθ=0 is nπ

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