Question 80734
{{{(sec x-2)(2sec x-1)=0}}}


{{{2sec^2(x)-sec(x)-4sec(x)+2=0}}} Foil


{{{2sec^2(x)-5sec(x)+2=0}}} Combine like terms

Let {{{y=sec(x)}}}

{{{2y^2-5y+2=0}}}

Now factor to solve for y (note: this solver uses x instead of y):


*[invoke solving_by_factoring 2, -5, 2]


Since we have the solutions


{{{y=1/2}}} or {{{y=2}}}


we can say


{{{sec(x)=1/2}}} or {{{sec(x)=2}}}


which is equivalent to 


{{{1/cos(x)=1/2}}} or {{{1/cos(x)=2}}}


Now invert both sides


{{{cos(x)=2/1}}} or {{{cos(x)=1/2}}}


Now take the arccosine of both sides to solve for x



{{{x=cos^(-1)(2/1)}}} or {{{x=cos^(-1)(1/2)}}}


Since the arccosine of 2 is undefined we must discard that answer. So our answer is 

{{{x=pi/3+pi*n}}} where n is an integer

or 

{{{x=-pi/3+pi*n}}} where n is an integer


which is equivalent in degrees:


{{{x=60+360*n}}} where n is an integer

or 

{{{x=-60+360*n}}} where n is an integer