How do I solve $sec(3x)-sqrt2 = 0$ algebraically?

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Answer 1 · 2018-04-28T15:46:15

$x= pi/12+2/3pin$
$x= (7pi)/2+2/3pin$
n is an element of all integers

Let $u$ be $3x$ :
$sec(u)-sqrt2=0$

$secu= sqrt2$

Apply reciprocal identity:
$1/cosu= sqrt2$

$cosu= 1/sqrt2= sqrt2/2$

$u= pi/4 +2pin$
$u= (7pi)/4+2pin$

Now replace $u$ with $3x$ and solve for x:

$3x=pi/4 +2pin$
$3x=(7pi)/4+2pin$

$x= pi/12+2/3pin$
$x= (7pi)/2+2/3pin$

Here's a graph:
graph{sec(3x)-sqrt2 [-10, 10, -5, 5]}

How do I solve sec(3x)-sqrt2 = 0sec(3x)-sqrt2 = 0 algebraically?