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

Textbook Question

Chapter 5, 5.3 - Problem 43 - Precalculus (3rd Edition, Ron Larson).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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`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.`

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