Solve each equation for 0<x<2π

3cos x-sec x + 3 = 0

Re-write as

3cosx - 1/cosx + 3 = 0

Multiply both sides by cox to remove cosx from denominator to get

3cos^2x - 1 + 3cosx = 0

Rearrange into standard form

3cos^2x + 3cosx - 1 = 0

Let x = cosx

Then

3x^2 + 3x - 1 = 0

Solve using quadratic formula to get

x = 0.2638

x = -1.2637 This you can discard because cosx cannot be less than -1

Now substitute cosx back in

cosx = 0.2638

x = cos^-1(0.2638) = 1.304 radians

or x = 2pi - 1.304 = 4.979 radians

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