`2cos(x/2) - sqrt(2) = 0` Solve the multiple-angle equation.

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

`2cos(x/2)-sqrt(2)=0,`

`2cos(x/2)=sqrt(2),`

`cos(x/2) = sqrt(2)/2.`

The general solution is:

`x/2 = +-arccos(sqrt(2)/2) + 2kpi,` `kinZZ.`

`arccos(sqrt(2)/2) = pi/4,` so the final answer is:

`x = +-pi/2+4kpi,` `kinZZ.`