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Mathematics

If 3 tan2 θ - 1 = 0, find cos 2θ, given that θ is acute.

Trigonometrical Ratios

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Answer

Given,

⇒ 3 tan2 θ - 1 = 0

⇒ tan2 θ = 13\dfrac{1}{3}

⇒ tan θ = 13\sqrt{\dfrac{1}{3}}

⇒ tan θ = ±13\pm \dfrac{1}{\sqrt{3}}

As, θ is acute.

∴ tan θ = 13\dfrac{1}{\sqrt{3}}

⇒ tan θ = tan 30°

⇒ θ = 30°.

cos 2θ = cos 60° = 12\dfrac{1}{2}

Hence, cos 2θ = 12\dfrac{1}{2}.

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