Mathematics

The key is to recognize that $\sin^8 x + \cos^8 x$ can be simplified using the substitution $u = \sin^2 x + \cos^2 x = 1$ and repeated applications of algebraic identities. By expressing higher powers in terms of $\sin^2 x \cos^2 x$, you'll reduce the equation to a polynomial in a single variable. Once you solve for that variable, you'll find the corresponding values of $x$ in the given interval by carefully counting solutions to basic trigonometric equations.

The key is to recognize that $\sin^8 x + \cos^8 x$ can be simplified using the substitution $u = \sin^2 x + \cos^2 x = 1$ and repeated applications of algebraic identities. By expressing higher powers in terms of $\sin^2 x \cos^2 x$, you'll reduce the equation to a polynomial in a single variable. Once you solve for that variable, you'll find the corresponding values of $x$ in the given interval by carefully counting solutions to basic trigonometric equations.