(i) `tanA+tan(180^(@)+A)+cot(90^(@)+A)+cot(360^(@)-A)=?`

(a) `0`
(b )`2tanA`
(c) `2cotA`
(d) `tanA-cotA`

(II) Prove `sec (270^@ – A) sec (90^@ – A) – tan (270^@ – A) tan (90^@ + A) + 1 = 0`

Explanation

### Step-by-Step Solution

**Given Expression:**
\[ \tan A + \tan(180^\circ + A) + \cot(90^\circ + A) + \cot(360^\circ - A) \]

**Step 1: Simplify \(\tan(180^\circ + A)\)**
- We know that \(\tan(180^\circ + A) = \tan A\) because the tangent function has a period of \(180^\circ\).

...