Question

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

Answer 1

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

Ответ: $\frac{ \pi }{2}+ \pi k,$ k∈Z.

Answer 2

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