The quadratic equation whose roots are sin<sup>2</sup> 18° and cos<sup>2</sup> 36°, is:
\(\sin 18° = \frac{\sqrt{5} - 1}{4}\), so \(\sin^2 18° = \frac{6 - 2\sqrt{5}}{16} = \frac{3 - \sqrt{5}}{8}\).
\(\cos 36° = \frac{\sqrt{5} + 1}{4}\), so \(\cos^2 36° = \frac{3 + \sqrt{5}}{8}\).
Sum of roots = \(\frac{6}{8} = \frac{3}{4}\). Product = \(\frac{9 - 5}{64} = \frac{1}{16}\).
Equation: \(x^2 - \frac{3}{4}x + \frac{1}{16} = 0\), that is, \(16x^2 - 12x + 1 = 0\).
Answer: (A)
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