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

**Answer:**

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

**Step by Step Explanation:**

- We know that, ^@ tan \theta = \sqrt{(sec^2 \theta - 1)} ^@
- Now replace value of ^@ sec\theta ^@ in above equation.

^@ tan \theta = \sqrt{ \left( \dfrac{ a } { b } \right)^2 - 1 } ^@ - Simplify ^@ RHS ^@ of above equation.

^@ tan\theta = \sqrt{ \dfrac{ a^2 - b^2 } { b^2 } } ^@