Question

if sec theta +tan theta=p,express sec theta,tan theta,sin theta in terms of p

Answer 1

I think we have to use:

\[\huge \color{green}{\sec^2 \theta - \tan^2 \theta = 1}\]

Answer 2

Or,

\[(\sec \theta - \tan \theta)(\sec \theta + \tan \theta) = 1\]

Answer 3

So,
\[\sec \theta - \tan \theta = \frac{1}{p}\]

Answer 4

Simply add them:

\[2\sec \theta = p + \frac{1}{p} \implies \frac{p^2+1}{p}\]

So,
\[\sec \theta = \frac{p^2 + 1}{2p}\]

Answer 5

Now subtract them you will get tan\(\theta\)...