`sec(4x) - 2 = 0` Solve the multiple-angle equation.

Textbook Question

Chapter 5, 5.3 - Problem 42 - Precalculus (3rd Edition, Ron Larson).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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`sec(4x)-2=0,`

`sec(4x)=2.`

Because `sec(x)=1/cos(x),` obtain `cos(4x) = 1/2.`

The general solution is

`4x=+-arccos(1/2)+2kpi,` `kinZZ.`

`arccos(1/2) = pi/3,` so the final answer is

`x=+-pi/12+(kpi)/2,` `kinZZ.`

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