Question 747130
{{{sec(x)=1/cos(x)}}} so
{{{sec(x)=cos(x)}}} --> {{{1/cos(x)=cos(x)}}} --> {{{(cos(x))^2=1}}}
A solution that gives {{{cos(x)=1}}} is {{{x=0}}}.
A solution that gives {{{cos(x)=-1}}} is {{{x=180^o}}} (or {{{x=pi}}} radians).
Those are the only solutions such that
{{{0<=x<360^o}}} (or {{{0<=x<2pi}}} if we measure angles in radians).
There is an infinite number of other solutions that can be found by adding/subtracting multiples of {{{360^o}}} (or {{{2pi}}} radians).
All solutions can be expressed as
{{{x=k*180^o}}} (or {{{x=k*pi}}}radians) with {{{k}}} being an integer.