Correct Answer: Option C

Explanation

\(\cos^{2} x (\sec^{2} x + \sec^{2} x \tan^{2} x)\)

= \(\cos^{2} x \sec^{2} x + \cos^{2} x \sec^{2} x \tan^{2} x\)

= \(1 + \tan^{2} x\)

= \(1 + \frac{\sin^{2} x}{\cos^{2} x}\)

= \(\frac{\cos^{2} x + \sin^{2} x}{\cos^{2} x}\)

= \(\frac{1}{\cos^{2} x} = \sec^{2} x\)

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