Question

Simplify the expression:

cos(2tan^(-1)x)


any help is appreciated =D

Answer 1

tan^-1 x = arctan x are the same thing

The angle "A" with a tangent of x has sin A = x/sqrt(x^2+1) and
cos A = 1/sqrt(x^2+1)

The cosine of twice that angle is
cos^2 A - sin^2 A = (1 - x^2)/(1 + x^2)

(1-x^2)/(1+x^2) is the answewr

Check: If x = 1,
A = tan^-1x = 45 degrees
2A = 90 degrees
cos 90 = 0, which agrees with (1-x^2)/(1+x^2)