Question 1082998
<pre><b>
{{{cot^2(pi/2-(x)) = sec(x) + 1}}}

Since {{{pi/2-(x)}}} is the complement of x,

{{{cot(pi/2-(x))=tan(x)}}}

{{{tan^2(x) = sec(x) + 1}}}

Since {{{1+tan^2(theta)=sec^2(theta)}}}, {{{tan^2(theta)=sec^2(theta)-1}}} 

{{{sec^2(x)-1=sec(x)+1}}}

{{{sec^2(x)-sec(x)-2=0}}}

{{{(sec(x)^""-2)(sec(x)^""+1)=0}}}

{{{sec(x)-2=0}}},  {{{sec(x)+1=0}}}

{{{sec(x)=2}}},  {{{sec(x)=-1}}}

For {{{sec(x)=2}}} using the unit circle,

{{{matrix(1,5,

x,""="",pi/3, ",",5pi/3)}}}

For {{{sec(x)=-1}}} using the unit circle,

{{{matrix(1,3,x,""="",pi)}}}

Three solutions.

Edwin</pre>