Question 1151425
<pre>
Picture yourself in a ’special’ world where 
{{{c^2+s^2=1}}}
Under this assumption, select the true statement/s:
<pre>We try out each possibility:</pre>
A) Every 
{{{1 + (s^2)/(c^2)}}} 
can be ’exchanged’ for 
{{{1^""/c^2}}}
<pre>We see if this equation
{{{1 + (s^2)/(c^2)=1^""/c^2}}}
is equivalent to the original.
We multiply through by the common denominator c²
{{{c^2*1 + c^2*expr((s^2)/(c^2))=c^2*expr(1^""/c^2)}}}
{{{c^2 + cross(c^2)*expr((s^2)/cross(c^2))=cross(c^2)*expr(1^""/cross(c^2))}}}
{{{c^2+s^2=1}}}
That is the correct choice.  But let's see why the other one is not correct</pre>
B) Every 
{{{(s^2)/(c^2)}}} 
can be ’exchanged’ for 
{{{1^""/c^2 - 1}}}
<pre>We see if this equation
{{{(s^2)/(c^2)=1^""/c^2 - 1}}}
is equivalent to the original.
We multiply through by the common denominator c²
{{{c^2*expr((s^2)/(c^2))=c^2*expr(1^""/c^2) - c^2*1}}}
{{{cross(c^2)*expr((s^2)/(cross(c^2)))=cross(c^2)*expr(1^""/cross(c^2)) - c^2}}}
{{{c^2 = cross(c^2)*expr((s^2)/cross(c^2))-cross(c^2)*expr(1^""/cross(c^2))}}}
{{{c^2=s^2-1}}}
And even if I subtract s² from both sides, I get
{{{c^2-s^2=-1}}}
that is not the same as the original.
So A) is the only correct answer.

Edwin</pre>