How do you find ALL solutions of the equation below in the interval [0, 2π) for $9sec^2(x)-12=0$ ?

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Answer 1 · 2015-05-03T22:38:11

$f(x) = 9.(1/cos^2 x) - 12 = 0,$ Let cos = t

$f(t) = 12t^2 - 9 = 3(4t^2 - 3) = 0$

$4t^2 = 3 -> t = (sqr3)/2, and t = -(sqr3)/2$

a. $t = cos x = (sqr3)/2$ -> x = 30 deg

b $x = -(sqr3)/2$ = 150 deg

Within interval (0, 2pi), there are 2answers: 30 and 150

How do you find ALL solutions of the equation below in the interval [0, 2π) for 9sec^2(x)-12=09sec^2(x)-12=0?