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Find the value of $x$ for which $(\sin A + \csc A)^2 + (\cos A + \sec A)^2 = x + \tan^2 A + \cot^2 A$
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$(\sin A + \csc A)^2 + (\cos A + \sec A)^2 = x + \tan^2 A + \cot^2 A \implies \sin^2 A + \csc^2 A + 2 + \cos^2 A + \sec^2 A + 2 = x + \tan^2 A + \cot^2 A \implies 1 + 2 + 2 + 1 + \cot^2 A + 1 + \tan^2 A = x + \tan^2 A + \cot^2 A \implies x = 7$.