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


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Answer:

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

Step by Step Explanation:
  1. 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} ^@
  2. 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} ^@

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