Question

Solve the following equations.
$4{\sin }^{4}x+{\cos }^{4}x=1$

Answer 1

${4\sin }^{4}x+{\cos }^{4}x=1$

${4\sin }^{4}x+{(1-{\sin }^{2}x)}^2=1$

${5\sin }^{4}x={2\sin }^{2}x$

Either, ${2\sin }^{2}x=0,\sin x=0,x=n\pi .$

or, $\sin x=\sqrt{\frac{5}{2}}⟹$ Not possible.

So, $x=n\pi .$