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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