Explanation

(c)
Given, $S_{n} = \cos^{n}{\theta + \sin^{n}\theta}$
$\therefore 3S_{4} - 2S_{6} = 3\left\lbrack \left( \cos^{4}{\theta + \sin^{4}\theta} \right) \right\rbrack - 2\lbrack\cos^{6}{\theta + \sin^{6}\theta}\rbrack$
$= 3\lbrack\left( \cos^{2}{\theta + \sin^{2}\theta} \right)^{2} - 2\sin^{2}{\theta\cos^{2}\theta}\rbrack$
$- 2\lbrack(\cos^{2}{\theta + \sin^{2}\theta})(\cos^{4}{\theta + \sin^{4}{\theta - \cos^{2}{\theta\sin^{2}\theta}}})\rbrack$
$= 3\left\lbrack 1 - 2\sin^{2}{\theta\cos^{2}\theta} \right\rbrack - 2\left( \cos^{2}{\theta + \sin^{2}\theta} \right)$
$\lbrack\left( \cos^{2}{\theta + \sin^{2}\theta} \right) - 3\cos^{2}{\theta\sin^{2}\theta}\rbrack$
$= 3 - 6\sin^{2}{\theta\cos^{2}{\theta - 2 + 6\cos^{2}{\theta\sin^{2}\theta}}}$
$= 1$