Question

$sin^{4} frac{x}{4} -cos x^{4} frac{x}{4} = frac{1}{2}$

Answer 1

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