Solve each equation for 0<x<2π
3cos x-sec x + 3 = 0
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
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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