Question 978429
{{{3 sec^2(x)-3 = 0 }}}
{{{3(sec^2(x)-1)=0}}}
Dividing by 3 to get an equivalent equation we get
{{{sec^2(x)-1=0}}}
Factoring we get
{{{(sec(x)+1)(sec(x)-1)=0}}}--->{{{system(sec(x)=-1,"or",sec(x)=1)}}}
{{{sec(x)=1/cos(x)=-1}}}<--->{{{cos(x)=-1}}} corresponds to {{{highlight(x=pi))))
{{{sec(x)=1/cos(x)=1}}}<--->{{{cos(x)=1}}} corresponds to {{{highlight(x=0)}}} .
The graphs of {{{red(cos(x))}}} and {{{green(sec(x))}}} look like this
{{{drawing(500,300,-1,7,-2,2,
line(2pi,-2,2pi,2),locate(6.3,0.5,2pi),arrow(pi,1.5,pi,-1),locate(3.05,1.72,pi),graph(500,300,-1,7,-2,2,cos(x),1/cos(x),1,-1) )}}}

{{{x=2pi}}} is also a solution, but is not within the interval {{{"[ 0 ,"}}}{{{2pi}}}{{{")"}}} , because the{{{")"}}} next to {{{2pi}}} means {{{x<pi}}} .
{{{highlight(x=0)}}} and {{{highlight(x=pi)}}} are the only two solutions with {{{0<=x<pi}}} .
The smaller solution is {{{highlight(x=0)}}} and the larger one is {{{highlight(x=pi)}}} .


NOTE:
I got a thank you message from you for my answer to a different question.
In that thank you, you were asking
"So I have the samller value 0 and what is the larger one?"
I am guessing that thank you was for htmentor's answer of this question.
I had not answered this question before I got your thank you.