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cos(2 arctan(x)) =

A1
B-x²
Cx
D(1-x²)/(1+x²) (cos 2θ = cos²θ - sin²θ = (1-x²)/(1+x²))
Answer & Solution
Correct answer: D. (1-x²)/(1+x²) (cos 2θ = cos²θ - sin²θ = (1-x²)/(1+x²))
We have cos 2θ = 2 cos²θ - 1. That is cos 2θ = 2/(1+x²) - 1. So cos 2θ = (1-x²)/(1+x²). Alternatively (1 - tan²θ)/(1+tan²θ).
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