How do you evaluate $sec(tan^-1(sqrt( 3)/(3)))$ ?

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Answer 1 · 2016-05-22T12:31:14

$sec(tan^(-1)(sqrt3/3))=+-2/sqrt3$

As $tan(npi+pi/6)=sqrt3/3$

$tan^(-1)(sqrt3/3)=pi/6$ or $tan^(-1)(sqrt3/3)=(7pi)/6$

Hence

$sec(tan^(-1)(sqrt3/3))=sec(pi/6)=2/sqrt3$ or

$sec(tan^(-1)(sqrt3/3))=sec((7pi)/6)=-2/sqrt3$

How do you evaluate sec(tan^-1(sqrt( 3)/(3)))sec(tan^-1(sqrt( 3)/(3)))?