Question

Solve ${\sin }^{4}x+{\cos }^{4}x=5/8$.

Answer 1

$1-2{\sin }^{2}x{\cos }^{2}x=5/8$
or $2-{\sin }^{2}2x=5/4$
$\therefore {\sin }^{2}2x=3/4$
$\therefore \sin 2x=\pm \sqrt{3}/2=\pm \sin \left(\pi /2\right)$
$\therefore 2x=n\pi \pm \frac{\pi }{3}$ or $x=\frac{n\pi }{2}\pm \frac{\pi }{6}$.