Question 153874
Simplify the expression.
Cos(2arctan(x)) 
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Use the double-angle formula cos(2w) = 1-2sin^2(w)
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In your problem w = arctan(x)
If the tangent of w is x/1 then the sin(w) = x/sqrt(x^2+1)
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So cos(2arctan(x)) = 1 - 2[x/sqrt(x^2+1)]^2 = 1 - 2[x^2/(x^2+1)]
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Cheers,
Stan H.