### If ^@ sec\theta + tan\theta = p, ^@ find value of ^@ sec\theta ^@ in terms of ^@ p. ^@

**Answer:**

^@ \dfrac{ 1 } { 2 } \left( p + \dfrac{ 1 } { p } \right) ^@

**Step by Step Explanation:**

- We know that,

^@ \begin{align} & sec^2\theta - tan^2\theta = 1 \\ \implies & (sec\theta + tan\theta) (sec\theta - tan\theta) = 1 \\ \implies & p(sec\theta - tan\theta) = 1 \\ \implies & sec\theta - tan\theta = \dfrac{ 1 } { p } \\ \end{align} ^@ - Now,

^@\begin{align} & (sec\theta + tan\theta) + (sec\theta - tan\theta) = p + \dfrac{ 1 } { p } \\ \implies & 2sec\theta = \left( p + \dfrac{ 1 } { p } \right) \\ \implies & sec\theta = \dfrac{ 1 }{ 2 } \left( p + \dfrac{ 1 } { p } \right) \end{align} ^@