Prove that: `(sin5A-sin3A)/(cos5A+cos3A)=tanA` (2)`(sinA+sin3A)/(cosA+cos3A)=tan2A`

Explanation

To prove the two statements, we will use trigonometric identities for the sum and difference of sines and cosines. Let's break down the solution step by step.

### Part 1: Prove that \((\sin 5A - \sin 3A) / (\cos 5A + \cos 3A) = \tan A\)

**Step 1: Apply the sine difference formula.**
We know that:
\[
\sin C - \sin D = 2 \cos\left(\frac{C + D}{2}\right) \sin\left(\frac{C - D}{2}\right)
...