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Prove the following identity, where the...

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`

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To prove the identity \((\sin A + \csc A)^2 + (\cos A + \sec A)^2 = 7 + \tan^2 A + \cot^2 A\), we will start by simplifying the left-hand side (LHS) and show that it equals the right-hand side (RHS). ### Step 1: Expand the LHS We start with the left-hand side: \[ LHS = (\sin A + \csc A)^2 + (\cos A + \sec A)^2 \] Expanding both squares: ...
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