Question 1173760
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{{{(sec(x)-1)(sec(x)+1) = 3}}}


{{{sec^2(x)-1 = 3}}} Difference of squares rule


{{{tan^2(x) = 3}}} Apply one of the pythagorean trig identities


{{{tan(x) = ""+-sqrt(3)}}} Apply the square root to both sides


{{{tan(x) = sqrt(3)}}} or {{{tan(x) = -sqrt(3)}}} Break up the plus minus into two separate equations


{{{x = arctan(sqrt(3))}}} or {{{x = arctan(-sqrt(3))}}} Arctangent is the same as inverse tangent.


{{{x = pi/3 + pi*n}}} or {{{x = -pi/3+pi*n}}} Use the unit circle. Note that tan(pi/3) = sqrt(3) and tan(-pi/3) = -sqrt(3). The {{{pi*n}}} portion is needed to capture all possible solutions for each arctan equation solved. 


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Answer:


The full solution set consists of x values such that
{{{x = pi/3 + pi*n}}} or {{{x = -pi/3+pi*n}}}
where n is any integer


One example solution is {{{x = pi/3 + 2pi}}}. In this case, we use n = 2 on the first equation shown above.
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