Question

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

Answer 1

-cosx=cosx
2cosx=0
cosx=0
x=π/2+πn,n∈z

Answer 2

$sin^2 (frac{x}{2})-cos^2 (frac{x}{2})=cosx \ \ -(cos^2( frac{x}{2} )-sin^2( frac{x}{2} )) =cosx \ \ -cos2*( frac{x}{2} )=cosx \ \ -cosx=cosx \ -cosx-cosx=0 \ -2cosx=0 \ cosx=0 \ x= frac{ pi }{2}+ pi k$,
k∈Z.

Ответ: $frac{ pi }{2}+ pi k,$ k∈Z.