Question

sec theta - tan theta =1/root3,sec theta=?

Answer 1

The answer is in the pic.

Answer 2

$\sec( \alpha ) - \tan( \alpha ) = \frac{1 }{ \sqrt{3} } \\ \sec( \alpha ) + \tan( \alpha ) = \sqrt{3} \\ ( { \sec( \alpha ) - \tan( \alpha ) ) }^{2} = ({ \sec( \alpha ) + \tan( \alpha ) })^{2} - 4 \sec( \alpha ) \tan( \alpha ) \\ {( \frac{1}{ \sqrt{3} }) }^{2} - ({ \sqrt{3} })^{2} = - 4 \sec( \alpha ) \tan( \alpha ) \\ \sec( \alpha ) \tan( \alpha ) = \frac{2}{9}$
adding first two equations we get
2secx= sqrt3+1/sqrt3
secx=sqrt3/2+1/2sqrt3