`sec^2 (x) - 4sec(x) = 0` Use inverse functions where needed to find all solutions of the equation in the interval `0,2pi)`.

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Borys Shumyatskiy eNotes educator| Certified Educator

sec^2(x)-4sec(x)=sec(x)*(sec(x)-4)=0.

So sec(x)=0 or sec(x)=4.

sec(x)=1/cos(x) and it is never zero. It is =4 when cos(x)=1/4. There are two solutions on (0, 2pi): arccos(1/4) and 2pi-arccos(1/4).

They are approximately 75.5° and 284.5°.