Prove the following identities: `(sinA+secA)^2+(cos"A"+"c o s e cA")^2=(1+secAcos e cA)^2` `cot^2A((secA-1)/(1+sinA))+sec^2A((sinA-1)/(1+secA))=0`

Explanation

To prove the given trigonometric identities, we will work step by step through each identity.

### Identity 1:
**Prove that**
\[ (\sin A + \sec A)^2 + (\cos A + \csc A)^2 = (1 + \sec A \csc A)^2 \]

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