If ^@ sec\theta + tan\theta = p, ^@ find value of ^@ sec\theta ^ | Math Question and Answer | Edugain New Zealand

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

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