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:
  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 } } ^@

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