Question

How do you simplify sec(arctan(4x))?

Answer 1

Refer to explanation

Explanation:

Set `t=arctan4x=>tant=4x=(4x)/1`

Now imagine a right triangle with perpendicular sides `1,4x`
hence from Pythagorean theorem the hypotenuse is

`c=sqrt(1^2+(4x)^2)=>c=sqrt(1+16x^2)`

Finally we have that

`sec(arctan4x)=sec(t)=(sqrt(1+16x^2))/1=sqrt(1+16x^2)`