Find cos 2θ, given that θ is acute.

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

Answer :

3 tan² θ – 1 = 0

3 tan² θ = 1

⇒ tan² θ = 1/3

⇒ tan θ = 1/√3 [θ is acute so tan θ is positive]

θ = 30°

cos 2θ = cos 2 × 30°

= cos 60° = ½

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