Prove that
`(i) sec^(2) theta + "cosec"^(2) theta = sec^(2) theta "cosec"^(2) theta `
`(ii) tan^(2) theta - sin^(2)theta = tan^(2)theta sin^(2)theta `
`(iii) tan^(2) theta + cot^(2)theta +2 = sec^(2) theta "cosec"^(2) theta `

Explanation

Let's prove the three parts of the question step by step.

### Part (i): Prove that \( \sec^2 \theta + \csc^2 \theta = \sec^2 \theta \csc^2 \theta \)

**Step 1:** Start with the left-hand side (LHS):
\[ \text{LHS} = \sec^2 \theta + \csc^2 \theta \]
...