Explanation

(d)
Given, $4\sin^{4}{x + \cos^{4}{x - 1 = 0}}$
$\Rightarrow \ 4\sin^{4}{x + \left( \cos^{2}{x - 1} \right)\left( \cos^{2}{x + 1} \right) = 0}$
$\Rightarrow \ \ 4\sin^{4}{x - \sin^{2}{x\left( 1 - \sin^{2}{+ 1} \right) = 0}}$
$\Rightarrow \ \sin^{2}{x\left( 5\sin^{2}{x - 2} \right) = 0}$
$\Rightarrow \ \ \sin{x = 0}$ or $\pm \sqrt{\frac{2}{5}}$
Hence, $x = n\pi$ is the required solution