If p and p' are the distances of the origin from the lines `x "sec" alpha + y " cosec" alpha = k " and " x "cos" alpha-y " sin" alpha = k`
`"cos" 2alpha, " then prove that 4p^(2) + p'^(2) = k^(2).`

Explanation

To prove that \( 4p^2 + p'^2 = k^2 \), we will first find the distances \( p \) and \( p' \) from the origin to the given lines using the formula for the distance from a point to a line.

### Step 1: Identify the lines and the point
We have the following lines:
1. \( x \sec \alpha + y \csc \alpha = k \)
2. \( x \cos \alpha - y \sin \alpha = k \cos 2\alpha \)

The point from which we need to find the distances is the origin \( O(0, 0) \).
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