Question

sin^4x/4-cos^4x/4=1/2

Answer 1

$sin^{4} frac{x}{4} -cos ^{4} frac{x}{4} = frac{1}{2}, (sin^{2} frac{x}{4} ) ^{2} -(cos^{2} frac{x}{4} )^{2} = frac{1}{2} , (sin^{2} frac{x}{4} +cos^{2} frac{x}{4} )*(sin^{2} frac{x}{4} -cos^{2} frac{x}{4} )= frac{1}{2}$

$1*(-(cos^{2} frac{x}{4} -sin^{2} frac{x}{4} )= frac{1}{2}$
cos(2*(x/4))=-1/2
cos(x/2)=-1/2

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