Explanation

(b)
We have, $3\left\lbrack \sin^{4}{\left( \frac{3\pi}{2} - \alpha \right) + \sin^{4}(3\pi + \alpha)} \right\rbrack - 2\left\lbrack \sin^{6}{\left( \frac{\pi}{2} + \alpha \right) + \sin^{6}(5\pi - \alpha)} \right\rbrack$
$= 3\left\lbrack \left( - \cos\alpha \right)^{4} + \left( - \sin\alpha \right)^{4} \right\rbrack - 2\left\lbrack \cos^{6}{\alpha + \sin^{6}\alpha} \right\rbrack$
$= 3\left\lbrack \left( \cos^{2}{\alpha + \sin^{2}\alpha} \right)^{2} - 2\sin^{2}{\alpha\cos^{2}\alpha} \right\rbrack - 2\left\lbrack \left( \cos^{2}{\alpha + \sin^{2}\alpha} \right)^{3} - 3\cos^{2}{\alpha\sin^{2}{\alpha\left( \cos^{2}{\alpha + \sin^{2}\alpha} \right)}} \right\rbrack$
$= 3 - 6\sin^{2}{\alpha\cos^{2}{\alpha - 2 + 6\sin^{2}{\alpha\cos^{2}\alpha}}}$
$= 3 - 2 = 1$