SOLUTION: Simplify the expression. Cos(2arctan(x)) arctan is just the inverse of tan Example tan^-1 i keep getting (1-x^2)/(1+x) althoutgh it keeps saying that its wrong

Question 153874: Simplify the expression.
Cos(2arctan(x))

arctan is just the inverse of tan Example tan^-1
i keep getting (1-x^2)/(1+x) althoutgh it keeps saying that its wrong
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Simplify the expression.
Cos(2arctan(x))
---------------------
Use the double-angle formula cos(2w) = 1-2sin^2(w)
--------------------------
In your problem w = arctan(x)
If the tangent of w is x/1 then the sin(w) = x/sqrt(x^2+1)
------------------------------
So cos(2arctan(x)) = 1 - 2[x/sqrt(x^2+1)]^2 = 1 - 2[x^2/(x^2+1)]
=================
Cheers,
Stan H.
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