How do you simplify $sec(tan^(-1)(x))$ ?

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Answer 1 · 2018-08-08T09:37:50

$sec(tan^(-1)(x))=sqrt(x^2+1)$

$sec(tan^(-1)(x))$

let $y=tan^(-1)(x)$

$x=tan(y)$

$x=sin(y)/cos(y)$

$x^2=sin(y)^2/cos(y)^2$

$x^2+1=(cancel(cos(y)^2+sin(y)^2)^(=1))/cos(y)^2$

$x^2+1=sec(y)^2$

$sqrt(x^2+1)=sec(y)=sec(tan^(-1)(x))$

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How do you simplify sec(tan^(-1)(x))sec(tan^(-1)(x)) ?