### If $sec \theta = \dfrac{ a } { b }$ and $90^\circ > \theta > 0^\circ,$ find value of $tan \theta.$

$\sqrt{ \dfrac{ a^2 - b^2 } { b^2 } }$

Step by Step Explanation:
1. We know that, $tan \theta = \sqrt{(sec^2 \theta - 1)}$
2. Now replace value of $sec\theta$ in above equation.
$tan \theta = \sqrt{ \left( \dfrac{ a } { b } \right)^2 - 1 }$
3. Simplify $RHS$ of above equation.
$tan\theta = \sqrt{ \dfrac{ a^2 - b^2 } { b^2 } }$