Question 1142428
<pre>
{{{ sec^2(x) - 2 = tan^2(x) }}}
{{{ (1/cos^2(x)) - 2 = sin^2(x)/cos^2(x) }}}
{{{  1 - 2cos^2(x) = sin^2(x) }}}
{{{  ( 1-cos^2(x) ) - cos^2(x) = sin^2(x) }}} 
{{{  sin^2(x)  - cos^2(x) = sin^2(x) }}}

Now we see that we are looking for {{{ -cos^2(x) = 0 }}} or just {{{ cos(x) = 0 }}} on  [ {{{ 0 }}}, {{{ 2pi }}} )

{{{ cos(x) = 0 }}} at  {{{ pi/2  }}} and {{{  3pi/2  }}} only


But {{{ cos^2(x)=0 }}} implies the original equation is undefined (look at the 2nd line from the top), thus there is {{{ highlight(matrix(1,2,NO, SOLUTION)) }}}.

Graphing we can see this, the zero crossings for cos(x) line up with undefined values for the other two functions:

{{{ graph(400,400, -0.2,6.28 , -5,5, (1/(cos(x)*cos(x)) - 2),  tan(x)*tan(x), cos(x)) }}}

{{{ green(tan^2(x)) }}},  {{{ red(sec^2(x)-2) }}}, {{{blue(cos(x)) }}}