How do you solve $3 {csc}^{2} x - 2 = 2$ $3 csc^2 x - 2 = 2$ ?

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How do you solve $3 {csc}^{2} x - 2 = 2$ $3 csc^2 x - 2 = 2$ ?

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Answer 1 · 2016-04-20T04:56:23

$\pm \frac{π}{6} + 2 k π$ $+- pi/6 + 2kpi$
$\pm \frac{5 π}{6} + 2 k π$ $+- (5pi)/6 + 2kpi$

Explanation:

Replace in the equation sec x by $(\frac{1}{cos x})$ $(1/(cos x))$
$\frac{3}{{cos}^{2} x} - 2 - 2 = 0$ $3/(cos^2 x) - 2 - 2 = 0$
$\frac{3 - 4 {cos}^{2} x}{{cos}^{2} x} = 0$ $(3 - 4cos^2 x)/(cos^2 x) = 0$
(Condition cos x different to zero)
$3 - 4 {cos}^{2} x = 0$ $3 - 4cos^2 x = 0$
${cos}^{2} x = \frac{3}{4}$ $cos^2 x = 3/4$
$cos x = \pm \frac{\sqrt{3}}{2}$ $cos x = +- sqrt3/2$
a. $cos x = \frac{\sqrt{3}}{2} - \to x = \pm \frac{π}{6}$ $cos x = sqrt3/2 --> x = +- pi/6$
b. $x = - \frac{\sqrt{3}}{2} - \to x = \pm \frac{5 π}{6}$ $x = -sqrt3/2 --> x = +- (5pi)/6$
General answers:
$x = \pm \frac{π}{6} + 2 k π$ $x = +- pi/6 + 2kpi$
$x = \pm \frac{5 π}{6} + 2 k π$ $x = +- (5pi)/6 + 2kpi$

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How do you solve $3 {csc}^{2} x - 2 = 2$ $3 csc^2 x - 2 = 2$ ?

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