convert 'sec(arctan4x)' into an algebra form

[icyhot2590]

converting into an algebraic form

sec(arctan4x)

would it be

sec(4/(1+(3x)^2)

 

[skeeter]

Re: sec(arctan4x)

converting into an algebraic form


sec(arctan4x)

would it be

sec(4/(1+(3x)^2)

no.

let y = arctan(4x) ... then tan(y) = 4x/1 = opposite/adjacent

using Pythagoras ... hypotenuse = sqrt(1 + 16x²)

sec(y) = hypotenuse/adjacent = sqrt(1 + 16x²)

 

[stapel]

would it be sec(4/(1+(3x)^2)

How did you arrive at this answer?

Please reply showing all of your work and reasoning. Thank you.

Eliz.