Question 1028124
Substitute according to the definitions and go from there.


{{{system(csc(x)=1/sin(x),sec(x)=1/cos(x),tan(x)=sin(x)/cos(x))}}}


Through two steps, obtain  {{{sin^2(x)+cos^2(x)+(sin^2(x))/(cos^2(x))}}}


{{{1+(sin^2(x))/(cos^2(x))}}}



.... or that can still be kept as {{{1+tan^2(x)}}}.
Looking for something simplified, you can find an identity involving sec(x), tan(x), and 1.  That might or might not give something to make your expression simpler.



Instead of that, the expression can go as
{{{cos^2(x)/cos^2(x)+sin^2(x)/cos^2(x)}}}
{{{(cos^2(x)+sin^2(x))/cos^2(x)}}}
{{{1/cos^2(x)}}}
and by recognizing the definition,
{{{highlight(sec^2(x))}}}