Question

Find a formula for cos(tan−1(2x)) in terms of x

Answer 1

`~\cos\left( \tan^(-1) 2x\right)\\\\\\=\cos \left[\cos^(-1) (1)/(√((2x)^2+1^2)) \right]~~~~~~~~~~~~~~~~~~~~~~~~~~;[\text{Pythagorean theorem}]\\\\\\=\cos \left( \cos^(-1) (1)/(√(4x^2 +1)) \right)\\\\\\=(1)/(√(4x^2 +1))`