Question

If $4{\sin }^{4}x+{\cos }^{4}x=1$, then find $x$.

Answer 1

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

or, $4{\sin }^{4}x+({\cos }^{2}x-1)({\cos }^{2}x+1)=0$

or, $4{\sin }^{4}x-{\sin }^{2}x(-1+{\sin }^{2}x)=0$

or, ${\sin }^{2}x(5{\sin }^{2}x-2)=0$

or, ${\sin }^{2}x=0$ or, $5{\sin }^{2}x-2=0$

or, $x=n\pi$ or $x={\sin }^{-1}\pm \sqrt{\frac{2}{5}}$. $n$ is an integer.