[tex] sin^{4} \frac{x}{4} -cos x^{4} \frac{x}{4} = \frac{1}{2} [/tex]

sin⁴(x/4)-cos⁴(x/4)=1/2(sin²(x/4))²-(cos²(x/4))²=1/2(sin²(x/4)+cos²(x/4))*(sin²(x/4)-cos²(x/4))=1/21*(-cos(2*(x/4)))=1/2cos(x/2)=-1/2x/2=+-(arccos(-1/2))+2πn, n∈Zx/2=+-(π-π/6)+2πn, n∈Z.    x/2=+-5π/6+2πn, n∈Z |*2x=+-5π/3+4πn, n∈Z