Question

Sin4 x/2 – cos4 x/2 = 1/2

Answer 1

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

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

$-cos(2*frac{x}{2})*1=frac{1}{2}$

$cos x=-frac{1}{2}$

$x=^+_-(pi-arccos frac{1}{2})+2*pi*k$

$x=^+_-(pi-frac{pi}{3})+2*pi*k$

$x=^+_-frac{2*pi}{3}+2*pi*k$

 

k  є Z