`3sec^2 (x) - 4 = 0` Solve the equation.

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mathace | (Level 3) Assistant Educator

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Solve the equation `3sec^2(x)-4=0`

`3sec^2(x)=4`

`sec^2(x)=4/3`

`sec(x)=+-sqrt(4/3)`

sec(x)=`+-2/sqrt(3)`

Because cosine and secant are reciprocal functions

`cos(x)=+-sqrt(3)/2`

`x=pi/6+pin`

`x=(5pi)/6+pin`