Sin^2 x/2-cos^2 x/2=cosx

-cosx=cosx2cosx=0cosx=0x=π/2+πn,n∈z

[latex]sin^2 (frac{x}{2})-cos^2 (frac{x}{2})=cosx \ \ -(cos^2( frac{x}{2} )-sin^2( frac{x}{2} )) =cosx \ \ -cos2*( frac{x}{2} )=cosx \ \ -cosx=cosx \ -cosx-cosx=0 \ -2cosx=0 \ cosx=0 \ x= frac{ pi }{2}+ pi k [/latex],k∈Z.Ответ: [latex] frac{ pi }{2}+ pi k, [/latex] k∈Z.