Prove that
`(i) (tan A+ sin A)/(tan A- sin A)= (sec A+1)/(sec A-1) `
` (ii) (cot A- cos A)/(cot A+ cos A)= ("cosec" A-1)/("cosec" A+1) `

Explanation

Let's solve the two parts of the question step by step.

### Part (i): Prove that
\[ \frac{\tan A + \sin A}{\tan A - \sin A} = \frac{\sec A + 1}{\sec A - 1} \]

**Step 1:** Rewrite \(\tan A\) in terms of \(\sin A\) and \(\cos A\).
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