Question

Помогите решить уравнение: -cosx + cos x/2 = 1

Answer 1

-cosx+cosx/2=1
1-2cos²x/2+cosx/2-1=0
-2cos²x/2+cosx/2=0
cosx/2(1-2cosx/2)=0
cosx/2=0⇒x/2=π/2+πn⇒x=π+2πn
cosx/2=1/2⇒x/2=+-π/3+2πn⇒x=+-2π/3+4πn