If `sec theta + tan theta = p`, prove that
(i)` sec theta =(1)/(2)(p+(1)/(p)) " (ii) "tan theta =(1)/(2)(p-(1)/(p)) " (iii) " sin theta =(p^(2)-1)/(p^(2)+1).`

Explanation

To prove the given identities based on the equation \( \sec \theta + \tan \theta = p \), we will follow a step-by-step approach.

### Step 1: Find \( \sec \theta - \tan \theta \)

From the identity \( \sec^2 \theta - \tan^2 \theta = 1 \), we can express it as:

\[
\sec^2 \theta - \tan^2 \theta = (\sec \theta + \tan \theta)(\sec \theta - \tan \theta) = 1
...