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

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

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Answer 1 · 2016-04-20T04:56:23

$+- pi/6 + 2kpi$
$+- (5pi)/6 + 2kpi$

Explanation:

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

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

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