Prove the following identity, where the angles involved are acute angles for which the expressions are defined.
(viii) `(sinA+cose c A)^2+(cosA+secA)^2=7+tan^2A+cot^2A`

Explanation

To prove the identity \((\sin A + \csc A)^2 + (\cos A + \sec A)^2 = 7 + \tan^2 A + \cot^2 A\), we will simplify the left-hand side step by step.

### Step 1: Expand the Left-Hand Side
We start with the left-hand side:
\[ (\sin A + \csc A)^2 + (\cos A + \sec A)^2 \]
Using the expansion formula \((a + b)^2 = a^2 + b^2 + 2ab\), we can expand both terms.
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